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# Fluid Mechanics Formula

Fluids are already an integral part of our daily life. Engineering allows us to explore the properties and importance of fluids for a number of new applications and various functions. Fluid mechanics will help us to understand the behaviour of fluid under various forces and at different atmospheric conditions. This topic will explain some important properties and fluid mechanics formula with examples. Let us learn it!

## What is Fluid Mechanics?

This field is studied in detail within the Civil Engineering as well as in Mechanical Engineering and Chemical Engineering. A substance which flows is called as fluid. All liquid and gaseous substances are considered fluids. Water, oil, and others are very important in our routine life as they are used for various applications. Also, as example water is used for the generation of electricity in hydroelectric power plants and thermal power plants.

Fluid Mechanics is that branch of science which covers the behaviour of fluids when they are in a state of motion or rest. As we know, whether the fluid is at rest or motion, it is subjected to various forces and external conditions. It behaves in such conditions as per its physical properties. So Fluid mechanics deals with three aspects of the fluid, which are static, kinematics, and dynamics aspects.

1. Fluid statics: This studies the fluid in the state of rest.
2. Fluid kinematics: The fluid in the state of motion is called as moving fluid. Its study is fluid kinematics.
3. Fluid dynamics: It studies the effect of all pressures including the external pressures on the moving fluid.

Some common applications of fluids are as follows,

• Hydroelectric Power Plants
• Hydraulic machines
• Automobiles
• Refrigerators and Air Conditioners
• Thermal Power Plants
• Fluids as a Renewable Energy Source
• Heat Engines

## Some Formula for Fluid Mechanics

1] The density of a sample at constant density: $$\rho = \frac{m}{V}$$

Where,

 $$\rho$$ density of fluid m Mass V Volume

2] Pressure: $$p = \frac{F}{A}$$

 p Pressure F force applied A area affected

3] The pressure at a depth h in a fluid of constant density: $$p = p_{0} + \rho gh$$

 p the pressure at height h $$p_0$$ the pressure at zero height g acceleration due to gravity $$\rho$$ fluid density

4] Volume flow rate: $$Q = \frac{dV}{dt}$$

 Q flow rate dV change in volume dt time period.

5] Viscosity: $$\eta = \frac{FL}{vA}$$

 $$\eta$$ fluid viscosity F Force L distance between the plates V constant velocity A area of the plate

## Solved Examples for Fluid Mechanics Formula

Q.1: The distance amid two pistons is 0.015 mm and the viscous fluid flowing through produces a force of 1.2 N per square meter to keep these two plates move at a speed 35 cm/s. Calculate the fluid viscosity in the middle of the plates? Use Fluid mechanics formula.

Solution: Given parameters:

Distance between plates, $$L = 0.015 mm = 0.015 \times 10^{-3} m$$

Viscous force, $$\frac {F}{A} = 1.2 N per square meter area$$

Speed, v = 35 cm per sec = 0.35 m per sec.

Now, applying the formula,

$$\eta = \frac{FL}{vA} \\$$

$$= \frac{F}{A} \times \frac {L}{v} \\$$

$$= 0.0514 \times 10^{-3} N sec \;per \;Sq\; m$$

Thus fluid viscosity is $$0.0514 \times 10^{-3} N sec \;per \;Sq\; m.$$

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