Changes in the osmolality of body fluids (changes as minor as 1% are sufficient) play the most important role in regulating AVP secretion. The receptors that monitor changes in osmolality of body fluids (termed osmoreceptors) are distinct from the cells that synthesize and secrete AVP, and are located in the organum vasculosum of the lamina terminalis (OVLT) of the hypothalamus. The osmoreceptors sense changes in body osmolality by either shrinking or swelling. When the effective osmolality of the plasma increases, the osmoreceptors send signals to the AVP synthesizing/secreting cells located in the supraoptic and paraventricular nuclei of the hypothalamus, and AVP synthesis and secretion are stimulated. Conversely, when the effective osmolality of the plasma is reduced, secretion is inhibited. Because AVP is rapidly degraded in the plasma, circulating levels can be reduced to zero within minutes after secretion is inhibited.

In this scenario, the osmolality of the plasma will decrease to an estimate of 2.5%, hence inhibition of AVP.

Stimulation of atrial stretch receptors is incorrect because the increase in plasma volume is still below the threshold for its activation.

Osmotic diuresis is incorrect because 5% dextrose is isotonic, hence osmotic diuresis is not probable.

Renin is inhibited when an excess of NaCl in the tubular fluid is sensed by the macula densa.

The Nernst equation is used to calculate the membrane potential at which the ions are in equilibrium across the cell membrane.

The normal resting membrane potential is -70 mV (not + 70 mV).

The equation is:
E = RT/FZ ln {[X]o
/[X]i}

Where:
E is the equilibrium potential
R is the universal gas constant
T is the absolute temperature
F is the Faraday constant
Z is the valency of the ion
[X]o is the extracellular concentration of ion X
[X]i is the intracellular concentration of ion X.

Skeletal muscle blood flow is in the range of 1-4 ml/min per 100 g when at rest. Blood flow can reach 50-100 ml/min per 100 g during exercise. With maximal vasodilation, blood flow can increase 20 to 50 times.

The adrenal medulla releases catecholamines and increases neural sympathetic activity during exercise. Normally, alpha-1 and alpha-2 would cause vasoconstriction in the muscle groups being used, but vasodilatory metabolites override these effects, resulting in a so-called functional sympathectomy. Local hypoxia and hypercarbia, nitric oxide, K+ ions, adenosine, and lactate are some of the stimuli that cause vasodilation.

However, the splanchnic and cutaneous circulations, which supply inactive muscles, vasoconstrict.

Sympathetic cholinergic innervation of skeletal muscle arteries is found in some species (such as cats and dogs, but not humans). Vasodilation is induced by stimulating smooth muscle beta-2 adrenoreceptors, but at rest, the alpha-adrenoreceptor effects of adrenaline and noradrenaline predominate. During exercise, the skeletal muscle pump promotes venous emptying, but it does not necessarily increase blood flow.

The minimal alveolar concentration (MAC) is the concentration of an inhalation anaesthetic agent in the lung alveoli required to stop a response to the surgical stimulus in 50% of the patient.

Following factors don’t affect the MAC of the inhaled anaesthetic agents:

Gender, acidosis, alkalosis, hypothyroidism, hyperthyroidism, body weight, serum potassium level, and the duration of the anaesthesia.

MAC increase in children, elevated temperature, high metabolic rate, sympathetic increase and chronic alcoholism.

MAC decrease in low temperature, low oxygen level, old age, hypotension (<40 mmHg), depressant drugs e.g. opioids and low level of catecholamines; alpha methyl dopa. Carbon dioxide O2 at the pressure > 120mmHg is being used in anesthetic-Hinkman as an additive effect to decrease MAC, however, increase concentration of CO2 activates the sympathetic system resulting the MAC increases.

The cardiac action potential has several phases which have different mechanisms of action as seen below:
Phase 0: Rapid depolarisation – caused by a rapid sodium influx.
These channels automatically deactivate after a few ms

Phase 1: caused by early repolarisation and an efflux of potassium.

Phase 2: Plateau – caused by a slow influx of calcium.

Phase 3 – Final repolarisation – caused by an efflux of potassium.

Phase 4 – Restoration of ionic concentrations – The resting potential is restored by Na+/K+ATPase.
There is slow entry of Na+into the cell which decreases the potential difference until the threshold potential is reached. This then triggers a new action potential

Of note, cardiac muscle remains contracted 10-15 times longer than skeletal muscle.

Different sites have different conduction velocities:
1. Atrial conduction – Spreads along ordinary atrial myocardial fibres at 1 m/sec

2. AV node conduction – 0.05 m/sec

3. Ventricular conduction – Purkinje fibres are of large diameter and achieve velocities of 2-4 m/sec, the fastest conduction in the heart. This allows a rapid and coordinated contraction of the ventricles

Hypoxic Pulmonary vasoconstriction (HPV) reflects the constriction of small pulmonary arteries in response to hypoxic alveoli (.i.e.; PO2 below 80-100mmHg or 11-13kPa).

These blood vessels become independent of the nerve stimulus, when blood with a high PO2 flows through the lung which contains a low alveolar PO2.

Thus a low PO2 within the alveoli has been shown to impact on hypoxic pulmonary vasoconstriction (HPV) more than a low PO2 within the blood.

HPV results in the blood flow being directed away from poorly ventilated areas of the lung and helps to reduce the ventilation/perfusion mismatch (not increase).

In animals, volatile anaesthetic agents can diminish HPV, while in adults, the evidence proves less persuading, in spite of the fact that it certainly doesn’t strengthen the effects.

HPV response will be suppressed by 20 parts per million (ppm) of nitric oxide.

Myoglobin is a haemoglobin-like, iron-containing pigment that is found in muscle fibres. It has a high affinity for oxygen and it consists of a single alpha polypeptide chain. It binds only one oxygen molecule, unlike haemoglobin, which binds 4 oxygen molecules.

The myoglobin ODC is a rectangular hyperbola. There is a very low P50 0.37 kPa (2.75 mmHg). This means that it needs a lower P50 to facilitate oxygen offloading from haemoglobin. It is low enough to be able to offload oxygen onto myoglobin where it is stored. Myoglobin releases its oxygen at the very low PO2 values found inside the mitochondria.

P50 is defined as the affinity of haemoglobin for oxygen: It is the PO2 at which the haemoglobin becomes 50% saturated with oxygen. Normally, the P50 of adult haemoglobin is 3.47 kPa(26 mmHg).

Foetal haemoglobin has 2 ? and 2 ?chains. The ODC is left shifted – this means that P50 lies between 2.34-2.67 kPa [18-20 mmHg]) compared with the adult curve and it has a higher affinity for oxygen. Foetal haemoglobin has no ? chains so this means that there is less binding of 2.3 diphosphoglycerate (2,3 DPG).

Carbon monoxide binds to haemoglobin with an affinity more than 200-fold higher than that of oxygen. This therefore decreases the amount of haemoglobin that is available for oxygen transport. Carbon monoxide binding also increases the affinity of haemoglobin for oxygen, which shifts the oxygen-haemoglobin dissociation curve to the left and thus impedes oxygen unloading in the tissues.

In sickle cell disease, (HbSS) has a P50 of 4.53 kPa(34 mmHg).

For this patient, his forced expiratory volume in 1 second (FEV1) will decrease at the same rate as a non-smoker.

There is a notable, but slow, decline in FEV1 when an individual reaches the age of 26. An average reduction of 30 mls every year in non-smokers, while a more significant reduction of 50-70 mls is observed in approximately 20% of smokers.

Considering the age of the patient, individuals who begin smoking cessation by the age of 60 are far less likely to achieve normal FEV1 levels, even in the next five years. It is expected that their FEV1 will be approximately 14% less than their peers of the same age.

An elevated arterial blood lactate level and an increase anion gap ([Na + K] – [Cl + HCO3]) of >20mmol gives rise to lactic acidosis. It can also be a result of overproduction and/or reduced metabolism of lactic acid.

The liver and kidney are the main sites of lactate metabolism, not skeletal muscle.

The two types of lactic acidosis that are known are:

Type A – due to tissue hypoxia, inadequate tissue perfusion and anaerobic glycolysis. These may be seen in cardiac arrest, shock, hypoxaemia and anaemia. The management of type A lactic acidosis involves reversing the underlying cause of the tissue hypoxia.

Type B – occurs in the absence of tissue hypoxia. Some of the causes of this include hepatic failure, renal failure, diabetes mellitus, pancreatitis and infection. Some drugs can also cause this lie aspirin, ethanol, methanol, biguanides and intravenous fructose.

The mainstay of treatment involves:
1. Optimising tissue oxygen delivery
2. Correcting the cause
3. Intravenous sodium bicarbonate

In resistant cases, peritoneal dialysis can be performed.

Prostaglandins do not play a major role in regulating RBF in healthy resting individuals. However, during pathophysiological conditions such as haemorrhage and reduced extracellular fluid volume (ECVF), prostaglandins (PGI2, PGE1, and PGE2) are produced locally within the kidneys and serve to increase RBF without changing GFR. Prostaglandins increase RBF by dampening the vasoconstrictor effects of both sympathetic activation and angiotensin II. These effects are important because they prevent severe and potentially harmful vasoconstriction and renal ischemia. Synthesis of prostaglandins is stimulated by ECVF depletion and stress (e.g. surgery, anaesthesia), angiotensin II, and sympathetic nerves.

Non-steroidal anti-inflammatory drugs (NSAIDs), such as ibuprofen and naproxen, potently inhibit prostaglandin synthesis. Thus administration of these drugs during renal ischemia and hemorrhagic shock is contraindicated because, by blocking the production of prostaglandins, they decrease RBF and increase renal ischemia. Prostaglandins also play an increasingly important role in maintaining RBF and GFR as individuals age. Accordingly, NSAIDs can significantly reduce RBF and GFR in the elderly.

Total body water (TBW) is about 50% to 70% in adults depending on how much fat is present. ECF is relatively contracted in an obese person.

The simple rule is 60-40-20. (60% of weight = total body water, 40% of body weight is ICF and 20% is ECF)

For this woman, the total body water is 36 litres (0.6 × 60). ECF is 12 litres (1/3 of TBW) and 24 litres (2/3 of TBW) is intracellular fluid .

Sodium concentration is approximately 135-145 mmol/L in the ECF.

The ECF is made up of both intravascular and extravascular fluid and plasma proteins is found in both.

The derived SI unit of force is Newton.
F = m·a (where a is acceleration)
F = 1 kg·m/s2

The joule (J) is a converted unit of energy, work, or heat. When a force of one newton (N) is applied over a distance of one metre (Nm), the following amount of energy is expended:

J = 1 kg·m/s2·m =
J = 1 kg·m2/s2 or 1 kg·m2·s-2

The unit of velocity is metres per second (m/s or ms-1).

The watt (W), or number of joules expended per second, is the SI unit of power:

J/s = kg·m2·s-2/s
J/s = kg·m2·s-3

Pressure is measured in pascal (Pa) and is defined as force (N) per unit area (m2):
Pa = kg·m·s-2/m2
Pa = kg·m-1·s-2

A decrease in the functional residual capacity (FRC) is the most important physiologic change to consider for such patients.

FRC is the sum of the expiratory reserve volume and the residual volume. It is the resting volume of the lung, and is an important marker for lung function. During this time, the alveolar pressure is equal to the atmospheric pressure. When morbidly obese individuals lie supine, the FRC decreases by as much as 40% because the abdominal contents push the diaphragm into the thoracic cavity.

Chest wall compliance is expected to reduce because of fat deposition surrounding adjacent structures.

Inspiratory reserve volume (IRV) is expected to increase, and peak expiratory flow is expected to decrease, however the decrease in FRC is more important to consider because of the risk of hypoxia secondary to premature airway closure and ventilation-perfusion mismatch.

The respiratory quotient is the ratio of CO2 produced to O2 consumed while food is being metabolized:

RQ = CO2 eliminated/O2 consumed

Most energy sources are food containing carbon, hydrogen and oxygen. Examples include fat, carbohydrates, protein, and ethanol. The normal range of respiratory coefficients for organisms in metabolic balance usually ranges from 1.0-0.7.

Granulated sugar is a refined carbohydrate with no significant fat, protein or ethanol content.

The RQ for carbohydrates is = 1.0

The RQ for the rest of the compounds are:

Fats RQ = 0.7
The chemical composition of fats differs from that of carbohydrates in that fats contain considerably fewer oxygen atoms in proportion to atoms of carbon and hydrogen.

Protein RQ = 0.8
Due to the complexity of various ways in which different amino acids can be metabolized, no single RQ can be assigned to the oxidation of protein in the diet; however, 0.8 is a frequently utilized estimate.

Adenosine receptors are expressed on the surface of most cells.
Four subtypes are known to exist which are A1, A2A, A2B and A3.

Of these, the A1 and A2 receptors are present peripherally and centrally. There are agonists at the A1 receptors which are antinociceptive, which reduce the sensitivity to a painful stimuli for the individual. There are also agonists at the A2 receptors which are algogenic and activation of these results in pain.

The role of adenosine and other A1 receptor agonists is currently under investigation for use in acute and chronic pain states.

Secreted T4 and T3 circulate in the bloodstream almost entirely bound to proteins. Normally only about 0.03% of total plasma T4 and 0.3% of total plasma T3 exist in the free state. Free T3 is biologically active and mediates the effects of thyroid hormone on peripheral tissues in addition to exerting negative feedback on the pituitary and hypothalamus. The major binding protein is thyroxine-binding globulin (TBG), which is synthesized in the liver and binds one molecule of T4 or T3. About 70% of circulating T4 and T3 is bound to TBGl 10% to 15% is bound to another specific thyroid-binding protein called transthyretin (TTR). Albumin binds 15% to 20%, and 3% to lipoproteins. Ordinarily only alterations in TBG concentration significantly affect total plasma T4 and T3 levels.

Two important biological functions have been ascribed to TBG. First, it maintains a large circulating reservoir of T4 that buffers any acute changes in thyroid gland function. Second, binding of plasma T4 and T3 to proteins prevents loss of these relatively small hormone molecules in urine and thereby helps conserve iodide. TTR transports T4 in CSF and provides thyroid hormones to the CNS.

During fetal development, blood oxygenated by the placenta flows to the foetus through the umbilical vein, bypasses the fetal liver through the ductus venosus, and returns to the fetal heart through the inferior vena cava.

Blood returning from the inferior vena cava then enters the right atrium and is preferentially shunted to the left atrium through the patent foramen ovale. Blood in the left atrium is then pumped from the left ventricle to the aorta. The oxygenated blood ejected through the ascending aorta is preferentially directed to the fetal coronary and cerebral circulations.

Deoxygenated blood returns from the superior vena cava to the right atrium and ventricle to be pumped into the pulmonary artery. Fetal pulmonary vascular resistance (PVR), however, is higher than fetal systemic vascular resistance (SVR); this forces deoxygenated blood to mostly bypass the fetal lungs. This poorly oxygenated blood enters the aorta through the patent ductus arteriosus and mixes with the well-oxygenated blood in the descending aorta. The mixed blood in the descending aorta then returns to the placenta for oxygenation through the two umbilical arteries.

CBF is defined as the blood volume that flows per unit mass per unit time in brain tissue and is typically expressed in units of ml blood/100 g tissue/minute. The normal average CBF in adults human is about 50 ml/100 g/min, with lower values in the white matter (,20 ml/100 g/min) and greater values in the gray matter (,80 ml/100 g/min).

Low CBF levels between 30-40 ml/100 g/min may begin to show poor prognostic EEG. EEG findings consistently associated with a poor outcome are isoelectric EEG, low voltage EEG, and burst suppression (specifically burst suppression with identical bursts), as well as the absence of EEG reactivity.

The measurements of GFR are done using renally inert indicators like inulin, where passive rate of filtration at the glomerulus = rate of excretion. Normal value is about 180 litres per day.

GFR is altered by renal blood flow but blood flow does not need to be measured.

The reabsorption of Na leads to a low excretion rate and low urine concentration and therefore its use as an indicator would lead to an erroneously LOW GFR.

If there is tubular secretion of any solute, the clearance value will be higher than that of inulin. This will be either due to tubular reabsorption or the solute not being freely filtered at the glomerulus.

Smoking is a major risk factor associated with perioperative respiratory and cardiovascular complications. Evidence also suggests that cigarette smoking causes imbalance in the prostaglandins and promotes vasoconstriction and excessive platelet aggregation. Two of the constituents of cigarette smoke, nicotine and carbon monoxide, have adverse cardiovascular effects. Carbon monoxide increases the incidence of arrhythmias and has a negative ionotropic effect both in animals and humans.

Smoking causes an increase in carboxyhaemoglobin levels, resulting in a leftward shift in which appears to represent a risk factor for some of these cardiovascular complications.

There are two mechanisms responsible for the leftward shift of oxyhaemoglobin dissociation curve when carbon monoxide is present in the blood. Carbon monoxide has a direct effect on oxyhaemoglobin, causing a leftward shift of the oxygen dissociation curve, and carbon monoxide also reduces the formation of 2,3-DPG by inhibiting glycolysis in the erythrocyte. Nicotine, on the other hand, has a stimulatory effect on the autonomic nervous system. The effects of nicotine on the cardiovascular system last less than 30 min.

Heme a exists in cytochrome a and heme c in cytochrome c; they are both involved in the process of oxidative phosphorylation. 5′-Aminolevulinic acid synthase (ALA-S) is the regulated enzyme for heme synthesis in the liver and erythroid cells.

There are two forms of ALA Synthase, ALAS1, and ALAS2.

In any alveolar unit, the V/Q ratio affects alveolar oxygen (PAO2) and carbon dioxide tension (PACO2).

The partial pressure of alveolar carbon dioxide (PACO2) is plotted against the partial pressure of alveolar oxygen in a Ventilation-Perfusion (V/Q) ratio graph (PAO2). Given a set of model assumptions, the curve represents all of the possible values for PACO2 and PAO2 that an individual alveolus could have.

In the case of an infinity V/Q ratio (ventilation but no perfusion or dead space), the PACO2 of the alveolus will equal zero, while the PAO2 will approach that of external air (150mmmHg). At the apex of the lung, the V/Q ratio is 3.3, compared to 0.67 at the base.

PACO2 and PAO2 approach the partial pressures for these gases in the venous blood when the V/Q ratio is zero (no ventilation but perfusion). At the base of the lung, the V/Q ratio is 0.67, whereas at the apex, it is 3.3.

PAO2 at the apex is typically 132mmHg, and PACO2 is typically 28mmHg.

The average PAO2 at the base is 89 mmHg, while the average PACO2 is 42 mmHg.

After the carotid body, the thyroid gland is the second most richly vascular organ in the body.

The global blood flow to the thyroid gland can be measured using:
1. Colour ultrasound sonography
2. Quantitative perfusion maps using MRI of the thyroid gland using an arterial spin labelling (ASL) method.

This table shows the blood flow to various organs of the body at rest:
Organ Blood Flow(ml/minute/100g)
Hepatoportal 58
Kidney 420
Brain 54
Skin 13
Skeletal muscle 2.7
Heart 87
Carotid body 2000
Thyroid gland 560

Human skeletal muscle is composed of a heterogeneous collection of muscle fibre types which differ histologically, biochemically and physiologically.

It can be biochemically classified into 2 groups. This is based on muscle fibre myosin ATPase histochemistry. These are:

Type 1 (slow twitch): Muscle fibres depend upon aerobic glycolytic metabolism and aerobic oxidative metabolism. They are rich in mitochondria, have a good blood supply, rich in myoglobin and are resistant to fatigue.

Type II (fast twitch): Muscle fibres are sub-divided into:
Type IIa – relies on aerobic/oxidative metabolism
Type IIb – relies on anaerobic/glycolytic metabolism.

Fast twitch muscle fibres produce short bursts of power but are more easily fatigued.

Cardiac and smooth muscle twitches are relatively slow compared with skeletal muscle.

During glycolysis, 2,3-diphosphoglycerate (2,3-DPG) is
created in erythrocytes by the Rapoport-Luebering shunt.

The production of 2,3-DPG increases for several conditions
in the presence of decreased peripheral tissue O2 availability.
Some of these conditions include hypoxaemia, chronic lung
disease anaemia, and congestive heart failure. Thus,
2,3-DPG production is likely an important adaptive mechanism.

High levels of 2,3-DPG cause a shift of the curve to the right.
Low levels of 2,3-DPG cause a shift of the curve to the left,
as seen in states such as septic shock and hypophosphatemia.

The number of osmoles (Osm) of solute per litre (L) of solution (Osmol/L) is the unit of measurement for solute concentration. The calculated serum osmolality assumes that the primary solutes in the serum are sodium salts (chloride and bicarbonate), glucose, and urea nitrogen.

2 (Na + K) + Glucose + Urea (all in mmol/L) = calculated osmolarity

313 mOsm/L = 2 (144 + 6) + 9.5 + 3.5

Sodium and potassium ions clearly contribute the most to plasma osmolarity. Glucose and urea, on the other hand, are less so.

The osmolarity of normal serum is 285-295 mOsm/L. Temperature and pressure affect osmolality, and this calculated variable is less than osmolality for a given solution.

The number of osmoles (Osm) of solute per kilogramme (Osm/kg) is a measure of osmolality, which is also a measure of solute concentration. Temperature and pressure have no effect on the value. An osmometer is used to measure it in the lab. Osmometers rely on a solution’s colligative properties, such as a decrease in freezing point or a rise in vapour pressure.

The osmolar gap (OG) is calculated as follows:

OG = osmolaRity calculated from measured serum osmolaLity

Excess alcohols, lipids, and proteins in the blood can all contribute to the difference.

Phosphate is the principal anion of the intracellular fluid, most of which is bound to either lipids or proteins. They dissociate or associate with different compounds, depending on the enzymatic reaction, thus forming a constantly shifting pool.

Calcium and magnesium are also present intracellularly, however in lesser amounts than phosphate.

Sodium is the most abundant extracellular cation, and Chloride and is the most abundant extracellular anion.

These clinical signs suggest that 15-30% of circulating blood volume has been lost.

Pelvic fractures are associated with significant haemorrhage (>2000 ml) that can be concealed. This may require aggressive fluid resuscitation which is initially with crystalloids and then blood. What is also important is including stabilisation of the fracture(s) and pain relief.

The Advanced Trauma Life Support (ATLS) classification of haemorrhagic shock is as follows:

Class I haemorrhage (blood loss up to 15%):
<750 ml of blood loss
Minimal tachycardia
No changes in blood pressure, RR or pulse pressure
Patients do not normally not require fluid replacement as will be restored in 24 hours, but in trauma, this needs to be correct.

Class II haemorrhage (15-30% blood volume loss):
Uncomplicated haemorrhage requiring crystalloid resuscitation
Represents about 750 – 1500 ml of blood loss
Tachycardia, tachypnoea and a decrease in pulse pressure (due to a rise in diastolic component due action of catecholamines).
There are minimal systolic pressure changes.
There may be associated anxiety, fright or hostility

Class III haemorrhage (30-40% blood volume loss):
Complicated haemorrhagic state – crystalloid and probably blood replacement are required
There are classical signs of inadequate perfusion, marked tachycardia, tachypnoea, significant changes in mental state and measurable fall in systolic pressure.
Almost always require blood transfusion, but decision based on patient initial response to fluid resuscitation.

Class IV haemorrhage (> 40% blood volume loss):
Preterminal event patient will die in minutes
Marked tachycardia, significant depression in systolic pressure and very narrow pulse pressure (or unobtainable diastolic pressure)
Mental state is markedly depressed
Skin cold and pale.
Needs rapid transfusion and immediate surgical intervention.

A blood loss of >50% results in loss of consciousness, pulse and blood pressure.

Fluid resuscitation following trauma is a controversial area.

This clinical scenario points to a 15-30% blood loss. However, further crystalloid and blood replacement may be required after assessing the clinical situation. There is increasing evidence to suggest that transfusion of large volumes of crystalloid in the hospital setting are likely to be deleterious to the patient and hypotensive resuscitation and judicious blood and blood product resuscitation is a more appropriate option. A ratio of 1 unit of plasma to 1 unit of red blood cells is used to replace fluid volume in adults.

This patient does not require immediate transfusion of O negative blood and there is time for a formal crossmatch. The argument about colloids versus crystalloids has existed for decades. However, while they have a role in fluid resuscitation, they are not first line.

There is a risk of anaphylaxis, Hypernatraemia, and acute renal injury with colloidal solutions.

A mercury barometer can be used to determine absolute pressure. A glass tube with one closed end serves as the barometer. The open end is inserted into a mercury-filled open vessel. The mercury in the container is pushed into the tube by atmospheric pressure exerted on its surface. Absolute pressure is the distance between the tube’s meniscus and the mercury surface.

Pressure is defined as force in newtons per unit area (F) (A). 

Mass of mercury = area (A) × density (ρ) × length (L)
Pressure = ((A × ρ × L) × 9.8 m/s2)/A
Pressure = ρ × L x 9.8
Pressure is proportional to L

The numerator and denominator of the above equation, area (A), cancel out. The constants are density and the gravitational acceleration value.

The length is proportional to the applied pressure.