Hydrostatic Paradox – An Introduction
When we break the word hydrostatic we get ‘hydro’ which means water and ‘static’ means something fixed or unchanged. Again the literal meaning of paradox is ‘contradiction’. So to sum it all up, the hydrostatic paradox is a state when containers with different shapes but have the same base, when filled with liquid of same height, then the force applied by the liquid on the container will be the same. However, the amount of water in each container would be different.
Break the words into smaller parts and you will understand the concepts by the means of the words themselves.
Keeping this in mind, the faculties at Vedantu have compiled all the details related to the topic in this particular article to give a better learning experience and to help the students perform well in their exams.
What will you learn from the article?
Hydrostatic Paradox - An introduction
Definition
Hydrostatic law
Hydrostatic Pressure
Frequently asked questions
Definition and meaning of Hydrostatic paradox
Hydrostatic paradox deals with the pressure of a liquid at all points of the same horizontal level (depth).
It is defined as:
“The hydrostatic pressure at a certain horizontal level of a liquid is directly proportional to the distance of the horizontal level from the surface of the liquid”.
The hydrostatic paradox states that the height of water in a container is independent of the shape of the container.
The height of fluid relative to the base of the container determines the pressure, and the pressure equilibrium determines the shape of fluid. Let us consider two containers ‘a’ and ‘b’ as shown below:
The pressure at a depth ‘h’ is the same at all horizontal points of the cylindrical container. Any element of fluid in the cylindrical container ‘a’ is always in equilibrium because the weight of the fluid element is balanced by the pressure difference of the fluid elements below it and above it.
For container ‘b’, the pressure of any fluid element at the edge is the same on the above side, like container ‘a’ but not on the below side.
The liquid pressure of the container is in equilibrium with outside atmospheric pressure. Hence, equal pressure is exerted on the fluid within. This pressure is not enough to maintain the equilibrium of fluid elements. Now, the question arises, how is the equilibrium of fluid at the edge explained?
This is explained as follows:
The walls of the container exert force on the fluid element based on the pressure at each point. In container ‘b’ the walls are slanted and offer an upward force that stabilizes the fluid elements next to it.
(Image will be uploaded soon)
The above figure represents the free-body diagram of fluid elements at the edge. The wall of the container exerts a diagonal force on the fluid element. The horizontal component of this force is balanced by the pressure exerted by the fluid. The vertical component of his force is balanced by outside atmospheric pressure.
Hydrostatic law
Hydrostatic law determines the amount of pressure exerted at any point of a given area of fluid, above a surface. It can also be defined as the total weight of this fluid on that surface.
Hydrostatic pressure is the increasing amount of pressure that is exerted on the water as depth increases. The French scientist Blaise Pascal gave a principle which states that “If one part of an object in water is pressurized, that pressure is transmitted throughout the entire body of water without diminishing.
This principle forms the basis of hydraulic systems, and it is applied in hydraulic pump systems. In a hydraulic system, the pressure of a column of water is placed on one side, to exert that pressure on the other side of the column.
For example, if a downward force is applied to the left side of a u-shaped pipe (having a valve), the valve applies pressure on the left arm causing the plate to move on the right arm. This force is used to lift heavy loads like cars, trucks, boats, cranes and other vehicles.
Hydrostatic Paradox Expression:
The mathematical expression of Hydrostatic Paradox is given by:
P ∝ h
Hydraulic Pressure
The formula for hydraulic fluid pressure is given by:
The fluid pressure at a depth h below the surface of any fluid is given by the formula-
P= Pa + 𝝆gh
Where,
P = pressure of the fluid at a depth h from the surface of the liquid/fluid.
Pa = atmospheric pressure.
𝝆 = mass density of the fluid/liquid.
g = acceleration due to gravity.
h = vertical height between the surface and the point.
Solved Example
Ques-Calculate the hydrostatic pressure of water at the bottom of a 7-meter pool. Given: density of water = 1000 kg/m3.
Ans- To find hydrostatic pressure, the following formula is used:
P = ρ * g * d
Where,
ρ = density of the liquid,
g = gravity, and
d = depth of the liquid.
We have,
P = 1000 * 9.8 * 7 = 68,600 Pa of hydrostatic pressure at a depth of a 7 meter pool.
Do you know?
Paradox definition- Paradox is an apparent contradiction to the physical descriptions of the universe. Some paradoxes are based on resolutions, while others are against the resolution and indicate flaws in the theory.
The shape of the container and the mass has no impact on the level of pressure of water
Hydraulic Pressure formula P= Pa + 𝝆gh
Solve more questions of the topic from the set of sample papers provided on the website and mobile app of Vedantu. Keep practising and keep learning.
FAQs on Hydrostatic Paradox
1.What is the simple reason behind the hydrostatic paradox?
The reason behind the hydrostatic paradox is that hydrostatic pressure is a function only of depth and not of volume. As logically it can be assumed that the concept of hydrostatic is of mass. Therefore no matter what is the shape of a container, if the level of water in all the containers with a similar base is brought up to the same level it will give equal pressure as a result. Hence, the term paradox is used to state the contradiction in the state of its appearance which logically gives a different answer than the actual reality.
2.What is the significance of studying the concept of hydrostatics?
The concept of hydrostatics explains various phenomena of everyday lives. It helps study the geographical phenomenon of change in atmospheric pressures with the change in altitude. It can explain why the woods or the oil floats on water. It also explains why the surface of the still water is always at the same level.
To know more about the topic you can read the full article on the topic of hydrostatic or you can also watch the video lecture of the particular article.
3.What do you mean by hydrostatic pressure?
In the study of fluid mechanics, Hydrostatic force is the force caused by the pressure of a liquid acting on submerged surfaces. In other words, it is the study of fluid that is in rest and to determine the pressure exerted on the submerged object. It is used in the case of storing and transportation of fluids. Thus, to avoid any spillovers or leakages. Also, it is used to measure blood pressure and measure other fluids in the body. It has usage in the field of meteorology, geography, etc.
4.What are the uses of hydraulics?
Hydraulics is used in many things. Here are some of the major uses of hydraulics.
The brakes of a car work on the mechanism of hydraulics. So, whenever you press the brake, the small piston in the break gets pressed along. The piston then applies a little pressure on the brake’s fluid. The fluid as a response puts some pressure on the pads of the large pistons of a break. When the brake pads come in contact with the brake drum, it slows down the car and eventually stops it.
Hydraulics is used in various other applications like -
Heavy Equipment, Airplanes, and jet planes adjusting wings Putting out/bringing in landing gear, Opening/closing doors, etc.
5. What are the differences between hydrostatic fluid & hydrodynamic fluid?
Some of the differences between hydrostatic fluid & hydrodynamic fluid are -
The Hydrostatic fluid transfers energy by power whereas the hydrodynamic fluid by relative motion.
The Hydrostatic fluid is static with respect to the surface of the container and the piston. Also, the oil and the piston are static to each other. While in the case of hydrodynamic, one parameter moves to cause others to accelerate or decelerate, thus, transferring energy.
Examples of hydrostatic fluid are gear pump, vane pump, piston pump, motors, and hydraulic cylinders. Hydrodynamic fluids are centrifugal pumps, fans, and fluid torque convertors.