Hydrostatic Pressure – Explanation and Applications

Fluid mechanics is a very important area in mechanical engineering. Fluid mechanics have also two areas which are fluid statics and fluid dynamics. In fluid dynamics, we are dealing with moving or flowing fluids. But in fluid statics, we are dealing with hydrostatic pressure. The importance of hydrostatic pressure is very great for engineers to design different kinds of systems. Here we explain the hydrostatic pressure in detail. Hydrostatic force is very important also.

So, it will be a very good start to fluid statics for you after reading and understanding this article.

What is Hydrostatic Pressure?

In the calculation of the hydrostatic pressure, we are dealing with the fluids at rest. So, only the normal forces that the weight of the fluid applies to the surfaces are important to us. And shear forces or wall shear forces are not important to us. Because there are no wall shear forces because of the moving fluids.

If we immerse a plane inside a fluid at rest perpendicularly, the pressure application of the fluid will increase with the increasing deepness. This is because the total weight of the fluid increases. So, if you dive into the deepness of the oceans, you will probably be squeezed by hydrostatic pressures.

So, the pressure distribution on the plane will be increasing order to the bottom sides. Because of it, the pressure at the top side of the plane is smaller than the pressure at the bottom side.

And also, the center of the pressure is more close to the bottom side.

If we think of the pressure distribution as a 2D triangular shape, the center of the pressure will pass from the center of gravity of this triangle.

Calculation of Hydrostatic Pressure

The calculation of the hydrostatic pressure is very simple. You just need to use the formula below to calculate the total pressure of the fluid in a specific depth;

You can remember this formula from the lessons in science classes. In this formula;

ρ is the density of the static fluid which has the unit of kg/m3 or lbf/ft3 in English units.

g is the gravitational acceleration which has the value of  9.81 m/s2 or 32.1741 ft/s2.

h is the total depth of the point where we want to measure the hydrostatic pressure. The unit is meters or ft.

If you use the units above, the unit of the pressure will be N/m2 or lbf/ft2.

As you see in the formula above, with the increasing density of the fluid, the pressure increases. This is because the total weight of the fluid increases. Also with the increasing depth, the pressure increases. And there is a right proportion between the hydrostatic pressure with the deepness. The pressure increases linearly with the increasing depth.

Also, we can add the atmospheric pressure to the hydrostatic pressure if we want to find the absolute pressure on a point in the static fluid.

Center of the Hydrostatic Pressure

In the hydrostatic pressure calculations, generally, we use the center pressure. And the total pressure on a place is equal to the center force times the total area. In general calculations, we use this approach in general. So, the center of gravity calculations is very important to us to calculate the hydrostatic pressures.

Hydrostatic Pressure Calculations on Submerged Plates

They are the most important calculations in fluid statics. We use lots of kinds of systems to calculate the hydrostatic pressures such as dams. So, we generally apply these calculations to the submerged planes;

They are the three important phases in which we calculate the hydrostatic pressures on themç In the first one, the plane is submerged into a specific fluid. And also, in the second one, the plate is submerged vertically. And in the third one, the plate is submerged horizontally.

We make our calculşations by using them.

We call the length of the plane ‘b’ and we call the total distance of the tip of the plane to the surface of the fluid ‘s’. And also we call the total deepness of the horizontal plate ‘h’. Furthermore, the total distance of the force to the surface of the fluid is ‘Yp’. You can see all these parameters above.

Tilted Plate

So, we can calculate the total force acting on the tilted plate with this formula;

So, there is an important parameter here which is the tilting angle θ. So the dependence of the total force on the deepness shows itself in the equation.

Vertical Plate

This is the situation where the plate dipped inside the fluid vertically. If you look at the formula, we do not need to consider the tilting angle here.

Horizontal Plate

In the horizontal direction, only the place o the force changes. Because hydrostatic pressure is all same on the plate.

There is no effect of any tilting.

Hydrostatic Pressure Calculator

There are lots of kinds of engineering applications in which we use hydrostatic pressure. So, we prepared a calculator that you can easily use in hydrostatic pressure calculations. Here, we explain how to use the hydrostatic pressure calculator below.

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The use of the calculator is very simple. You just need to select the orientation of the plate; tilted, horizontal, or vertical. After selecting the orientation, you need to enter the required variable that appears in the calculator. The variables are that we defined above.

And also, you need to enter the area of the plate. And then, click on the ‘Calculate!’ button to see the total hydrostatic pressure. If you want to make another calculation, click on the ‘Reset’ button.

Calculating Hydrostatic Forces on Curved Surfaces

In general, we deal with the curved surfaces that suböerged in the fluid in engineering. For example dams. The surfaces of the dams are curved in the shape. So, while we are making our calculations, we need to consider the hydrostatic forces on the dam structure.

The calculation is very simple. You can use the force reflection method.

Think about there being a curved surface in the fluid. You just need to draw the opposing flat walls against this curved surface to obtain a closed structure. And if you calculate the hydrostatic forces on these opposite walls, you can find the X and Y components of the forces acting on this curved wall.

The hydrostatic force that you calculated for the horizontal wall gives the Y component of the total force. And the vertical wall will give the X component of the total force. You just need to calculate the resultant force of the hydrostatic force on the curved surface.

Applications That We Use Hydrostatic Pressure

There are different kinds of practical and engineering applications that we use the hydrostatic pressure calculations.

Dams

Dams structures are so important in applications that we use hydrostatic pressure calculations. Because they are highly static applications. In the structural calculations of dams, we need to consider the hydrostatic forces acting on the wall.

If you check the structures of dams, the surface of these structures is in a convex shape to the water. So, it provides extra structural stability.

We calculate the total hydrostatic pressure effect on the walls of the dams by using the calculation methods that we explained above.

Glasses of Submarines and Ship Compartments

Also, if you check the design of the glasses of submarines and ship compartments in the water, they have a very strong structure and are round. This is because their design of them is for the hydrostatic pressure application.

The designers calculate the general effects of the hydrostatic pressure effects on the glasses and design these glasses according to the pressures.

Deep Sea Observers

If you take a look at the footage of Titanic lagan on the floor of the Atlantic Ocean, some devices are taking this footage. And the average deepness of this lagan is 3500 meters which are so deep. So, an ordinary device that we use in daily applications will not withstand hydrostatic forces at that level.

But the design of the deep sea observers is very sturdy in structure to withstand these so high forces and pressures to work in that deepness.

Old Water Towers

In the old towns, you probably see the water towers at the highest point of a hill. The water of the low-populated areas is saved inside this tower. And this tower is somehow big to contain enough water for all population.

There is a reason for the placement of this tower at the highest point. The main reason is, that this highness provides extra hydrostatic pressure to rush the water in our faucets at very high pressure. So, instead of the pumping power, we use the high elevation pressure for flowing the water from faucets.

Conclusion on Hydrostatic Pressure

As you see above, the term hydrostatic pressure is somehow basic. The calculation of them and the application of them into practical applications are very common.

So, you can understand that deepness is very important in hydrostatic pressure. With the increasing deepness, this pressure increases.

Also, you can use the calculator above to calculate hydrostatic pressures on different planes in the water or other fluids.

There are lots of important engineering applications in which we use hydrostatic pressure.

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