Fundamentals of Physics/Fluid Mechanics

Any substance that flows is called a fluid. In other words fluids cannot undergo shearing or tensile stress. This chapter is dedicated to studying about the behavior (mechanism) of fluids. Fluid mechanism is a vital science and is used in hydraulic engineering, aviation etc. There are two major branches in fluid mechanics, namely, fluid statics which is the study of fluid in a stationary state and fluid dynamics which is the study of fluid when its flowing, like what happens when water flows? So lets dive into fluid mechanics.

Fluids are readily able to flow because their intermolecular forces are comparatively week at room temperatures. Fluids do not have any specific shape and take the shape of the container into which they are filled. Fluids like air has no definite shape and are extremely turbulent.

Pressure

Fig 15-1 Schematic of device used to measure pressure under fluid

All fluids exert a force on any substance that's immersed in them. This is called pressure. Pressure compresses any object that is immersed in a fluid. Pressure in a fluid can be measured using a device as shown in figure 15-1. This device consists of a evacuated cylinder with a tight fitting piston. The piston's inward movement into the cylinder is resisted by the spring.

When the cylinder is immersed in the water, force acts upon the piston and pushes it inside the cylinder. If we had calibrated the spring properly, we could tell how much pressure is exerted on the piston by measuring its position in the cylinder.

Lets see how to calculate pressure. Mathematically pressure is equal to the force exerted on a object per unit area. That is

$P={\frac {F}{A}}N/m^{2}$

So lets say that radius of the piston is $r$ meters, then pressure is

$P={\frac {F}{\pi r^{2}}}$

Let say the piston has moved inward about a distance of $x$ meters from its normal position. Then the force on piston is equal to

$F=Kx$

Where K is a constant. Hence pressure is

$P={\frac {Kx}{\pi r^{2}}}N/m^{2}$

The unit of force is Newtons ($N$) and unit for area is meter-square ($m^{2}$). Pressure is force per unit area and hence has the unit Newton per meter-square ($N/m^{2}$). In honor of the great mathematician Blaise Pascal, pressure is called Pascal.