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Fluid statics: Hydrostatic Pressure Made Simple

Imagine water taking a well-deserved nap, completely still. That's what hydrostatics studies: the chill side of water, not the crazy rapids or splashing waves.

Here's where it gets interesting:

Civil engineers: Figuring out how much push water gives when it's all piled up in giant tanks or dams. This helps them build strong enough walls to keep the water happy in its home.

Submarine builders: Picture a sub going down, down, down. The water gets squished tighter, making a super squeeze. Hydrostatics helps design subs that can handle all that pressure without going pop!

The design of dams and submarines to resist hydrostatic forces in itself is a large topic and needs separate writings (In future hopefully) to grasp fully. However, a general introduction to this branch of fluid mechanics is given here.

This science is ancient. A guy named Archimedes figured it all out over 2,000 years ago! He basically cracked the code for understanding how much force still water exerts, and it's pretty much the same today.



Pressure: The key to it all

Pressure is the term which is used to describe the force applied on a unit area of an object. In mathematical terms simply:



Now those familiar with physics know that this will have units of N/(m^2). where, N= newtons (measure of force) and m^2(unit of area). But in simpler terms it is the distribution of force (or weight) over an area. 

Comparison between force and Pressure

A very interesting thing about this formula is it allows us to tell that a woman wearing high heels stepping on your foot will hurt more than an elephant doing the same. All because an elephants foot will exert weight distributed on a larger area. So, a woman's weight under the heel is relatively focused at a point. This is the difference between force and pressure. Just a matter of area.

A fun exercise the reader can do is assume the the weight of elephant say 49KN and weight of a woman as 0.59KN. Assume area of an elephants foot as 0.07m^2  and assume area of shoe heel as 0.0001m^2.
Simply use the formula to find the pressure under the elephants foot and a woman's heel. 

Do note that we are talking about 1 foot for both cases so do mind only taking 1/4 of elephants weight (4 legs!) and 1/2 the woman's weight( 2 legs!).

Understanding Hydrostatic Pressure

Just like solid things exert pressure water having its weight also does the same. Having previous introduction to pressure it becomes intuitive to grasp the concept of hydrostatic pressure. Imagine you go for a dive in a swimming pool, at first you dive at about 1m deep you will fell a pressure exerted on you. Now, go 5 m deep and so on. Notice the amount of water above you increases as you go down thus you will have to bear more weight exerted on the area of your body with each descent. this is the hydrostatic pressure. This is the pressure a still standing water exerts on the objects immersed in it thus the name static!.

As you've noticed in the above scenario hydrostatic pressure is a function of depth ( the deeper you go the stronger it becomes).

So hydrostatic pressure can be calculated using a simple formula:



The density of water is constant (1000 kg/m^3), g is constant ( 9.81 m/s^2) and h will vary depending upon the specific situation. 


Problem:
Suppose a rectangular tank for water is 3m deep. The base area is measured to be 3m by 2m. Find the force on the base of the tank.

This problem can be solved by finding the hydrostatic pressure using the above equation and simply multiplying it by the area of the bottom of the tank. 


I will discuss some other specialized applications of this in future.











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