How does hydrostatic pressure vary with the depth of any fluid?

Hydrostatic pressure always increases with the increasing depth of any fluid.

What is the hydrostatic paradox?

The hydrostatic paradox claims that the depth at a particular pressure is uniform irrespective of the shape and size of the container

Where is hydrostatic pressure employed?

Hydrostatic pressure is applied in such systems as dams, submarines, hydraulic presses, and other natural occurrences, such as that of ocean pressure at any depth.

What is the difference between hydrostatic pressure and fluid pressure?

Hydrostatic pressure and fluid pressure differ in that hydrostatic pressure specifically deals with stationary fluids, while fluid pressure encompasses stationary as well as moving fluids.

Frequently Asked Questions

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Learn About Buoyant Force

The buoyant force is a fundamental term in physics that explains why the floating and sinking of objects submerged in fluids take place. This upward force is exerted by the fluid, which might be water or air on an object partially or fully immersed in it.

Explore Some Hydraulic Machines

A hydraulic machine is a device that uses fluid to generate, control, and transmit power. Hydraulic machines can be found in many industries...

Explore: The Hydrostatic Paradox

The meaning of the Hydrostatic Paradox is that pressure at any depth is independent of the size, shape, and aspect of the container, with the liquid's

Master Newton's Law of Viscosity

Viscosity is a measurement of the resistance of a fluid to flow or deformation. It measures how much fluid resists the motion of sliding layers past one another. There is a...

Difference Between EMF and Voltage

Electromotive Force (EMF) and voltage are key to the functioning of electrical devices and systems. EMF measures the energy supplied by a...

Principles of Communication

The principles of communication are essential concepts that facilitate effective information exchange among individuals, groups, and systems. In

Periodic Motion: An Overview

Any motion that repeats at regular time intervals is known as periodic motion or harmonic motion.

Hydrostatic Pressure

Hydrostatic pressure is the pressure resulting from fluids at rest; it increases with depth. Its magnitude depends on the fluid's density and the force of gravity acting on it. Hydrostatic pressure is important in several fields: water systems, engineering, and biology.

1.0What is Hydrostatics?

Hydrostatic is the term given to fluids at rest. It refers to the understanding of forces and pressures within stationary fluids, especially liquids. Hydrostatics pertains to the effects of gravity on fluids that do not move.

2.0Principle of Hydrostatics

The principle of hydrostatic states that a fluid at rest experiences an increase in pressure with depth because of the weight of the fluid above. It acts equally in all directions and depends on fluid density and gravitational pull. The intensity of hydrostatic pressure is independent of the shape of the container since it depends only on depth, fluid density, and gravity.

3.0Hydrostatic Pressure

Hydrostatic pressure in 12th chemistry refers to the pressure exerted by a liquid at rest due to the weight of the liquid above it. Hydrostatic pressure is dependent on the depth of the liquid and the density of the liquid, as well as the gravitational force.

While in Physics Hydrostatics pressure is part of fluid mechanics dealing with fluids at rest. Science primarily examines the forces and pressures a fluid may exert upon an object and surfaces that are in equilibrium.

Hydrostatic Law of Pressure

According to the hydrostatic law of pressure, the pressure exerted at a given point by the fluid is proportional to the fluid's density and the acceleration due to gravity; it depends on the depth, or height, of the fluid above the given point where it exerts pressure. Mathematically, it can be expressed as:

$P = ρ g h$

Here:

P = Hydrostatic Pressure (in pascals, Pa)
ρ = Density of the fluid (in kg/m³)
g = Acceleration due to gravity (9.8 m/s²)
h = Depth of the fluid (in meters)
The S.I. unit of Hydrostatic Pressure is Pascal.

4.0Derivation of Hydrostatic Pressure Formula

To Prove: $P = ρ h g$

Solution: Imagine a column of water with the total volume V and A as the base surface area.

We know that:

$W e i g h t (W) = M a ss (m) \times A cce l er a t i o n d u e t o g r a v i t y (g)$

$W = m g$

And

$De n s i t y = \frac{ma ss}{V o l u m e}$

$ρ = \frac{m}{V} or m = ρ \times V$

Therefore,

Derivation of Hydrostatic Pressure Formula

$W = ρ V g$

We know that Volume is basically the product of surface area and height. Hence,

$V = A h$

$W = ρ A h g$

$P ress u re = \frac{F orce}{A re a}$

$P = \frac{ρ A h g}{A}$

$P = ρ h g$

5.0Hydrostatic Pressure and Fluid Pressure

Hydrostatic Pressure

Fluid Pressure

Hydrostatic pressure is a special case of fluid pressure. Hydrostatic pressure only pertains to fluids at rest. The Mathematical formula for Hydrostatic pressure is:

$P = ρ h g$

Fluid pressure may be defined as the force per unit area exerted by any fluid, such as liquid or gas. The Mathematical formula for Hydrostatic pressure is:

$P = F / A$

Both pressures are similar but hydrostatic pressure is particularly where the fluid is stationary under gravity.

6.0Solved Examples

Problem 1: A pressure gauge is placed at the bottom of a tank filled with a liquid of unknown density. The height of the liquid column is 12 meters, and the pressure at the bottom is measured to be 1.2×10⁵ Pa. Calculate the density of the liquid. (Atmospheric pressure is 1.01×10⁵Pa)

Solution: The pressure at the bottom of the tank is the sum of atmospheric pressure and hydrostatic pressure.

$P_{t o t a l} = P_{a t m} + P_{h y d ros t a t i c}$

$P_{h y d ros t a t i c} = 1.2 \times 1 0^{5} - 1.01 \times 1 0^{5}$

$P_{h y d ros t a t i c} = 0.19 \times 1 0^{5} P a$

Now, for solving the density of fluid:

$P_{h y d ros t a t i c} = ρ g h$

$ρ = \frac{P _{h y d ros t a t i c}}{g h}$

$ρ = \frac{0.19 \times 1 0 ^{5}}{9.8 \times 12}$

$= \frac{19000}{117.6} \approx 161.56 k g / m^{3}$

Problem 2: A vertical pipe is open at both ends and contains water. It is 20 meters high. Calculate the velocity of the water flowing from the top of the pipe if the water is at rest at the bottom. Assume the water surface at the top of the pipe is open to the atmosphere.

Solution: For solving this question we can use Bernoulli’s equation here. Bernoulli's principle says the total pressure remains constant, meaning:

$P_{t o p} + \frac{1}{2} v_{t o p}^{2} + ρ g h_{t o p} = P_{b o tt o m} + \frac{1}{2} ρ v_{b o tt o m}^{2} + ρ g h_{b o tt o m}$

It is given that the velocity at the bottom is zero (v_bottom =0), and P_top= P_bottom, the equation will now become:

$ρ g h_{t o p} = \frac{1}{2} ρ v_{t o p}^{2}$

$v_{t o p} = 2 g h_{t o p}$

$= 2 \times 9.8 \times 20 = 392.4 \approx 19.8 m / s$

Problem 3: A steel tank is submerged 30 meters underwater. The tank has a spherical shape with a radius of 2 meters. Calculate the total force acting on the spherical surface due to the hydrostatic pressure.

Solution: The formula for force acting on a spherical surface submerged in a fluid is given by the formula:

$F = P_{a v er a g e} A$

Where

$P_{a v er a g e} = ρ g h$ and A = Area of sphere = $4 π r^{2}$

$A re a = 4 \times \frac{22}{7} \times 2 = 50.27 m^{2}$

$P_{a v er a g e} = ρ g h$

$P_{a v er a g e} = 1000 \times 9.8 \times 30 = 294000 P a$

$F = P_{a v er a g e} A$

$F = 294000 \times 50.27$

$= 1, 47, 79, 380 N = 14.78 MN$

Join ALLEN!

(Session 2026 - 27)

Name

Mobile Number

Class

Choose class

Goal

Choose your goal

Preferred Programs

Preferred Mode

State

Choose State

I agree to

I authorise ALLEN Career Institute Pvt Ltd to send me regular updates via Phone calls, Whatsapp, SMS, Robocalls (Automated Calls), Emails, or on postal address.

Learn About Buoyant Force

The buoyant force is a fundamental term in physics that explains why the floating and sinking of objects submerged in fluids take place. This upward force is exerted by the fluid, which might be water or air on an object partially or fully immersed in it.

Explore Some Hydraulic Machines

A hydraulic machine is a device that uses fluid to generate, control, and transmit power. Hydraulic machines can be found in many industries...

Explore: The Hydrostatic Paradox

The meaning of the Hydrostatic Paradox is that pressure at any depth is independent of the size, shape, and aspect of the container, with the liquid's

Master Newton's Law of Viscosity

Viscosity is a measurement of the resistance of a fluid to flow or deformation. It measures how much fluid resists the motion of sliding layers past one another. There is a...

Difference Between EMF and Voltage

Electromotive Force (EMF) and voltage are key to the functioning of electrical devices and systems. EMF measures the energy supplied by a...

Principles of Communication

The principles of communication are essential concepts that facilitate effective information exchange among individuals, groups, and systems. In

Periodic Motion: An Overview

Any motion that repeats at regular time intervals is known as periodic motion or harmonic motion.

Hydrostatic Pressure

Hydrostatic pressure is the pressure resulting from fluids at rest; it increases with depth. Its magnitude depends on the fluid's density and the force of gravity acting on it. Hydrostatic pressure is important in several fields: water systems, engineering, and biology.

1.0What is Hydrostatics?

Hydrostatic is the term given to fluids at rest. It refers to the understanding of forces and pressures within stationary fluids, especially liquids. Hydrostatics pertains to the effects of gravity on fluids that do not move.

2.0Principle of Hydrostatics

The principle of hydrostatic states that a fluid at rest experiences an increase in pressure with depth because of the weight of the fluid above. It acts equally in all directions and depends on fluid density and gravitational pull. The intensity of hydrostatic pressure is independent of the shape of the container since it depends only on depth, fluid density, and gravity.

3.0Hydrostatic Pressure

Hydrostatic pressure in 12th chemistry refers to the pressure exerted by a liquid at rest due to the weight of the liquid above it. Hydrostatic pressure is dependent on the depth of the liquid and the density of the liquid, as well as the gravitational force.

While in Physics Hydrostatics pressure is part of fluid mechanics dealing with fluids at rest. Science primarily examines the forces and pressures a fluid may exert upon an object and surfaces that are in equilibrium.

Hydrostatic Law of Pressure

According to the hydrostatic law of pressure, the pressure exerted at a given point by the fluid is proportional to the fluid's density and the acceleration due to gravity; it depends on the depth, or height, of the fluid above the given point where it exerts pressure. Mathematically, it can be expressed as:

$P = ρ g h$

Here:

P = Hydrostatic Pressure (in pascals, Pa)
ρ = Density of the fluid (in kg/m³)
g = Acceleration due to gravity (9.8 m/s²)
h = Depth of the fluid (in meters)
The S.I. unit of Hydrostatic Pressure is Pascal.

4.0Derivation of Hydrostatic Pressure Formula

To Prove: $P = ρ h g$

Solution: Imagine a column of water with the total volume V and A as the base surface area.

We know that:

$W e i g h t (W) = M a ss (m) \times A cce l er a t i o n d u e t o g r a v i t y (g)$

$W = m g$

And

$De n s i t y = \frac{ma ss}{V o l u m e}$

$ρ = \frac{m}{V} or m = ρ \times V$

Therefore,

$W = ρ V g$

We know that Volume is basically the product of surface area and height. Hence,

$V = A h$

$W = ρ A h g$

$P ress u re = \frac{F orce}{A re a}$

$P = \frac{ρ A h g}{A}$

$P = ρ h g$

5.0Hydrostatic Pressure and Fluid Pressure

Hydrostatic Pressure

Fluid Pressure

Hydrostatic pressure is a special case of fluid pressure. Hydrostatic pressure only pertains to fluids at rest. The Mathematical formula for Hydrostatic pressure is:

$P = ρ h g$

Fluid pressure may be defined as the force per unit area exerted by any fluid, such as liquid or gas. The Mathematical formula for Hydrostatic pressure is:

$P = F / A$

Both pressures are similar but hydrostatic pressure is particularly where the fluid is stationary under gravity.

6.0Solved Examples

Problem 1: A pressure gauge is placed at the bottom of a tank filled with a liquid of unknown density. The height of the liquid column is 12 meters, and the pressure at the bottom is measured to be 1.2×10⁵ Pa. Calculate the density of the liquid. (Atmospheric pressure is 1.01×10⁵Pa)

Solution: The pressure at the bottom of the tank is the sum of atmospheric pressure and hydrostatic pressure.

$P_{t o t a l} = P_{a t m} + P_{h y d ros t a t i c}$

$P_{h y d ros t a t i c} = 1.2 \times 1 0^{5} - 1.01 \times 1 0^{5}$

$P_{h y d ros t a t i c} = 0.19 \times 1 0^{5} P a$

Now, for solving the density of fluid:

$P_{h y d ros t a t i c} = ρ g h$

$ρ = \frac{P _{h y d ros t a t i c}}{g h}$

$ρ = \frac{0.19 \times 1 0 ^{5}}{9.8 \times 12}$

$= \frac{19000}{117.6} \approx 161.56 k g / m^{3}$

Problem 2: A vertical pipe is open at both ends and contains water. It is 20 meters high. Calculate the velocity of the water flowing from the top of the pipe if the water is at rest at the bottom. Assume the water surface at the top of the pipe is open to the atmosphere.

Solution: For solving this question we can use Bernoulli’s equation here. Bernoulli's principle says the total pressure remains constant, meaning:

$P_{t o p} + \frac{1}{2} v_{t o p}^{2} + ρ g h_{t o p} = P_{b o tt o m} + \frac{1}{2} ρ v_{b o tt o m}^{2} + ρ g h_{b o tt o m}$

It is given that the velocity at the bottom is zero (v_bottom =0), and P_top= P_bottom, the equation will now become:

$ρ g h_{t o p} = \frac{1}{2} ρ v_{t o p}^{2}$

$v_{t o p} = 2 g h_{t o p}$

$= 2 \times 9.8 \times 20 = 392.4 \approx 19.8 m / s$

Problem 3: A steel tank is submerged 30 meters underwater. The tank has a spherical shape with a radius of 2 meters. Calculate the total force acting on the spherical surface due to the hydrostatic pressure.

Solution: The formula for force acting on a spherical surface submerged in a fluid is given by the formula:

$F = P_{a v er a g e} A$

Where

$P_{a v er a g e} = ρ g h$ and A = Area of sphere = $4 π r^{2}$

$A re a = 4 \times \frac{22}{7} \times 2 = 50.27 m^{2}$

$P_{a v er a g e} = ρ g h$

$P_{a v er a g e} = 1000 \times 9.8 \times 30 = 294000 P a$

$F = P_{a v er a g e} A$

$F = 294000 \times 50.27$

$= 1, 47, 79, 380 N = 14.78 MN$

Frequently Asked Questions

How does hydrostatic pressure vary with the depth of any fluid?

What is the hydrostatic paradox?

Where is hydrostatic pressure employed?

What is the difference between hydrostatic pressure and fluid pressure?

Frequently Asked Questions

How does hydrostatic pressure vary with the depth of any fluid?

What is the hydrostatic paradox?

Where is hydrostatic pressure employed?

What is the difference between hydrostatic pressure and fluid pressure?

Join ALLEN!

Related Articles:-

Learn About Buoyant Force

Explore Some Hydraulic Machines

Explore: The Hydrostatic Paradox

Master Newton's Law of Viscosity

Difference Between EMF and Voltage

Principles of Communication

Periodic Motion: An Overview

Hydrostatic Pressure

1.0What is Hydrostatics?

2.0Principle of Hydrostatics

3.0Hydrostatic Pressure

Hydrostatic Law of Pressure

4.0Derivation of Hydrostatic Pressure Formula

5.0Hydrostatic Pressure and Fluid Pressure

6.0Solved Examples

Table of Contents

Join ALLEN!

Related Articles:-

Learn About Buoyant Force

Explore Some Hydraulic Machines

Explore: The Hydrostatic Paradox

Master Newton's Law of Viscosity

Difference Between EMF and Voltage

Principles of Communication

Periodic Motion: An Overview

Hydrostatic Pressure

1.0What is Hydrostatics?

2.0Principle of Hydrostatics

3.0Hydrostatic Pressure

Hydrostatic Law of Pressure

4.0Derivation of Hydrostatic Pressure Formula

5.0Hydrostatic Pressure and Fluid Pressure

6.0Solved Examples

Table of Contents