# Flow With Turbine

## Problem 20 - Bernoulli's Energy Theorem

**Problem 20**

The 600-mm pipe shown in Figure 4-11 conducts water from reservoir A to a pressure turbine, which discharges through another 600-mm pipe into tailrace B. The loss of head from A to 1 is 5 times the velocity head in the pipe and the loss of head from 2 to B is 0.2 times the velocity head in the pipe. If the discharge is 700 L/s, what power is being given up by the water to the turbine and what are the pressure heads at 1 and 2?

## Energy and Head of Flow

Energy is defined as ability to do work. Both energy and work are measured in Newton-meter (or pounds-foot in English). Kinetic energy and potential energy are the two commonly recognized forms of energy. In a flowing fluid, potential energy may in turn be subdivided into energy due to position or elevation above a given datum, and energy due to pressure in the fluid. Head is the amount of energy per Newton (or per pound) of fluid.

Kinetic Energy and Velocity Head

Kinetic energy is the ability of a mass to do work by virtue of its velocity. The kinetic energy of a mass M having a velocity v is ½Mv^{2}. Since M = W/g,

$\text{Velocity head} = \dfrac{K.E.}{W} = \dfrac{v^2}{2g}$

Elevation Energy and Elevation Head

In connection to the action of gravity, elevation energy is manifested in a fluid by virtue of its position or elevation with respect to a horizontal datum plane.

$\text{Elevation head} = \dfrac{\text{Elevation energy}}{W} = z$

Pressure Energy and Pressure Head

A mass of fluid acquires pressure energy when it is in contact with other masses having some form of energy. Pressure energy therefore is an energy transmitted to the fluid by another mass that possesses some energy.

$\text{Pressure head} = \dfrac{\text{Pressure energy}}{W} = \dfrac{p}{W}$