Question

Bernoulli's theorem is applied to:

Answer 1

Bernoulli's theorem:

1. Bernoulli's theorem simply states that if the fluid flows horizontally without any inclination so that there is no change in its potential energy, then a small reduction in fluid pressure is directly associated with an increase in the velocity of the fluid.
2. The Bernoulli equation also states that the total energy of flowing fluid per unit mass, at any point is the summation of the kinetic, potential, and fluid-pressure energies and is equal to a constant value throughout the liquid.
3. One simple example of Bernoulli's principle is the lift created by an aircraft wing.
4. The rounded shape of the wing on the top surface and the slight inclination allows the air to move faster on top of the wing than below it.
5. Hence, the pressure on the top is much less compared to the lower part, thereby allowing an upward net force to act on the wing as well as on the aircraft.
6. Mathematically, Bernoulli's theorem may be written as,
7. $P_1+\frac{1}{2}\rho {v^2}_1+\rho g{h}_1=P_2+\frac{1}{2}\rho {v^2}_2+\rho g{h}_2$, where $P,v,h$are pressure, velocity, and height at the corresponding positions $1$ and $2$ respectively.
8. Or in its simple form $\Rightarrow \frac{P}{\rho }+gh+\frac{1}{2}{v}^2=$Constant.
9. Bernoulli's relation gives the accurate relationship between the height, velocity, and pressure in a moving fluid, for which, the viscosity and compressibility are very negligible and the flow is steady throughout.
10. Thus Bernoulli's theorem applies to incompressible flows.

Hence, Bernoulli's theorem is applied to the incompressible liquid in a streamlined flow.