## Mechanical Properties of Fluids

# Bernoullis principle and its applications

- An ideal fluid is that which incompressible, irrotational non viscous called ideal fluid.
- Bernoullis theorem states that the sum of the pressure energy kinetic energy and potential energy at any point in steady flow calculated per unit mass is constant.
- Bernoullies theorem represents law of conservation of energy.
- When flow is horizontal, height is same and hence sum of pressure head and velocity head is constant.
- When the speed of flow is zero every where Bernoullies theorem changes as P
_{1}− P_{2}= ρg(h_{2}−h_{1}) - The velocity of efflux of a liquid through an orifice is equal to that of the velocity acquired by a freely falling body from a height which is equal to that of the liquid level from orifice.
- Horizontal range is maximum when the orifice is at the middle.
- The plane motion of a spinning ball gets charged due to an effect called magnus effect.
- Atomiser, paint gun and bunsen burner work on the basis of Bernoullies theorem.
- Verturimeter is an ideal device of measuring rate of flow of liquid through pipe.
- Reynold number is the ratio of inertial force to viscous force.
- Blowing of roofs in heavy wind, Aeroplanes Aerodynamic lift magnus effect of spinning ball are applications of Bernoullies theorem.

### Bernoulli's principle and its applications View the Topic in this video From 0:40 To 22:35

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1. **Bernoulli's theorem**: If an ideal fluid is flowing in streamlined flow, then total energy, i.e., sum of pressure energy, kinetic energy and potential energy per unit volume of the liquid remains constant at every cross-section of the tube.

\tt \frac{p}{\rho g}+\frac{v^{2}}{2g}+h=constant

2. **Toricelli's theorem: **Velocity of efflux, v = \sqrt{2gh}

3. Venturimeter is a device to measure the flow speed of incompressible fluid.

Rate of flow of liquid, v = \tt \sqrt{\frac{2\rho_{m} gh}{\rho}}\left[\left(\frac{A}{a}\right)^2-1\right]^{-1/2}