Pressure in Drops
Let’s consider a liquid drop which is having a pressure P1; on comparing its pressure with the atmospheric pressure Patm, we found that P1 > Patm.
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This happens due to surface tension.
The surface of the body behaves as if covered by a stretched membrane having tension in all directions parallel to the surface that the pressure of liquid increases within a bubble.
Consider the free-body diagram of a liquid drop, as shown in Fig.
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If the force due to surface tension at the circumference is balanced by the pressure forces inside the drop, then:
2πRσ = PπR2
We get: ΔP = 2σ/R
Here, ΔPis the pressure difference between inside the drop and outside.
What is Blood Pressure?
Our heart pumps blood, oxygen, and nutrients through the arteries in our body.
Blood pressure is the measure of the force exerted by the circulating blood against our arterial walls.
There Are Two Readings Which Measure Blood Pressure, Which Are
Systolic blood pressure
Diastolic blood pressure
Systolic blood pressure is the higher number. It measures the force of blood being pumped around our body when our heart contracts.
Diastolic blood pressure is the lower number. It measures when the heart relaxes between beats.
The normal bp value is 120 mm Hg/80 mmHg.
Where mmHg stands for millimeters of mercury.
High BP
High blood pressure is always higher than the normal range of the bp.
It is also known as hypertension.
Its value is 140 mmHg / 90 mmHg or higher.
BP Drop
The value of bp, 90 mmHg/60 mmHg or lower is considered to be lower bp or bp drop.
Bp drop is also known as hypotension.
A Sudden Drop in Blood Pressure
A sudden drop in blood pressure happens when your organs don't get the proper amount of blood and oxygen.
According to the American Heart Association, we don't have fixed readings for specifying low bp.
However, medical experts say that our bp is low when systolic bp is less than 90 mmHg diastolic bp is less than 60.
So, if bp measures 84 mmHg/57 mmHg; it means our bp is low.
The Consequences of a Sudden Drop in BP Are
Dizziness or light-headedness
This happens when our brain doesn’t get enough supply of blood.
2. Fainting
Insufficient supply of blood to the brain can cause us to lose consciousness.
3. Blurred vision
4. Lack of concentration
5. Unable to focus on anything
Bp drop diminishes attention.
6. Memory nausea
We may feel discomfort, uneasiness, or an urge to vomit, and
7. Rapid breathing
8. Breath becomes shallow and breathing rate per minute increases.
The heart compensates for the lack of blood by pumping faster.
9. Fatigue
Tired or not wanting to do any physical activity.
BP Drops During Exercise
Blood pressure is measured by multiplying cardiac output and the total peripheral resistance.
Bp can change in response to an activity, body size, and diet.
It may happen due to health problems like obesity, or because of the blood vessel disease.
Bp is internally managed by baroreceptors, enlarged arteries that can detect changes in the blood pressure, and alert our nervous system to release hormones that constrict or dilate the vessels as per the requirement.
According to the Hemodynamics of Hypertension report, the type and duration of the exercise, how much water we lose through sweat, and in-case we exercise in the heat are factors that can usher to a drop in blood pressure.
However, if our bp persistently drops when we go from lying down to sitting up or from sitting to standing, we may have an orthostatic drop in blood pressure or postural bp drop.
Postural Hypotension Drop
The age-factor is the cause of postural hypotension.
Let’s assume an old person seated or lying down just like a bottle resting on the table as shown below:
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The blood is uniformly distributed in the body.
Now, if he suddenly stands up, due to the gravity effect, the blood tends to pool in the lower part of his body.
Just like we drink some amount of water, the remaining quantity rests at the lower part of the bottle.
Now, if he certainly stands up, the blood pools in the lower part (because of gravitational pooling), his upper part may not get enough blood.
This, in turn, may lead to a deficiency in the supply of blood and oxygen to cerebral ischemia, resulting in vertigo dizziness.
Therefore, to compensate postural hypotension, his heart pumps at a higher rate to bring the bp at a normal level.
Postural Drop in Blood Pressure
While measuring our bp, we could see a drop from 120/80 to 100/70 within minutes of changing your position.
Do You Know?
According to Langdon’s position, if we suddenly stand or sit, 600 to 700 ml, our blood is reduced in the upper part of the body because of pulling in the lower part of the body.
FAQs on Pressure In Drops, Bubbles, And Capillary Rise
1. What is the fundamental reason for excess pressure inside a liquid drop?
The excess pressure inside a liquid drop exists due to the phenomenon of surface tension. The liquid surface behaves like a stretched membrane, constantly trying to minimise its surface area. This creates an inward force on the liquid molecules. To counteract this inward pull and maintain equilibrium, the pressure inside the drop must be greater than the pressure outside. This difference is known as excess pressure.
2. What are the formulas for calculating excess pressure in a liquid drop and a soap bubble?
The formulas for excess pressure depend on the number of free surfaces. According to the CBSE Class 11 syllabus for 2025-26, the key formulas are:
- For a liquid drop (one free surface): The excess pressure is given by ΔP = 2σ/R.
- For a soap bubble (two free surfaces): The excess pressure is given by ΔP = 4σ/R.
Here, ΔP is the excess pressure, σ (sigma) is the surface tension of the liquid, and R is the radius of the drop or bubble.
3. Why is the excess pressure inside a soap bubble double that of a liquid drop of the same radius?
The excess pressure in a soap bubble is double that of a liquid drop because a bubble has two free surfaces in contact with air—an inner surface and an outer surface. Both surfaces contribute to the total surface tension effect, effectively doubling the inward force that needs to be balanced by internal pressure. In contrast, a liquid drop has only one free surface, so the pressure required to counteract the surface tension is half that of a bubble of the same size.
4. What is capillary rise and how is it explained?
Capillary rise, or capillarity, is the phenomenon of a liquid's surface rising or falling in a narrow tube (a capillary tube) relative to the surrounding liquid level. This happens due to the interplay of cohesive forces (attraction between liquid molecules) and adhesive forces (attraction between liquid and tube molecules). When adhesive forces are stronger than cohesive forces (e.g., water in a glass tube), the liquid 'wets' the surface and rises. The height (h) of the rise is given by the formula: h = (2σ cosθ) / (ρgr), where σ is surface tension, θ is the angle of contact, ρ is the liquid's density, g is acceleration due to gravity, and r is the tube's radius.
5. What are some real-world examples of capillary action?
Capillary action is a crucial phenomenon with many real-world applications. Some common examples include:
- The wick of an oil lamp drawing oil upwards to the flame.
- A piece of blotting paper absorbing ink.
- The upward movement of water from the roots to the leaves in plant stems.
- A sponge soaking up water against gravity.
- The ability of a towel to dry a wet surface.
6. What is the key difference between cohesive and adhesive forces in relation to surface tension phenomena?
The key difference lies in the types of molecules they act between:
- Cohesive Force: This is the force of attraction between similar molecules. For example, the force that holds water molecules together is a cohesive force. It is responsible for a liquid's tendency to form a spherical drop.
- Adhesive Force: This is the force of attraction between dissimilar molecules. For example, the force between water molecules and the glass molecules of a tube is an adhesive force.
The balance between these two forces determines whether a liquid will wet a surface and exhibit capillary rise or depression.
7. Why does mercury in a glass capillary tube show capillary depression instead of a rise?
Mercury shows capillary depression (the level inside the tube is lower than outside) because its cohesive forces are much stronger than its adhesive forces with glass. The strong attraction between mercury atoms pulls the liquid inward, away from the glass walls. This causes the meniscus to be convex (curved outwards) and results in the liquid level being depressed to minimise contact with the tube's surface.
8. How is the formula for excess pressure in a liquid drop (ΔP = 2σ/R) derived?
The derivation involves balancing forces on a hemispherical section of the drop. The steps are:
- Imagine cutting a liquid drop of radius R into two halves.
- The force due to surface tension acts along the circumference of the cut, trying to pull the two halves together. This force is F_tension = σ × (Circumference) = σ × (2πR).
- The force due to excess pressure (ΔP) acts on the circular area of the cut, pushing the two halves apart. This force is F_pressure = ΔP × (Area) = ΔP × (πR²).
- For the drop to be in equilibrium, these two forces must be equal: F_pressure = F_tension.
- Therefore, ΔP × πR² = σ × 2πR.
- Solving for ΔP, we get ΔP = 2σ/R.
