Oil of specific gravity 0.9 is flowing at the rate of 100 litres per second in a 0.30 m diameter pipe. If the pressure head at point P is 3 m of oil and this point P is 4 m above the datum line, then what will be the total energy at point P in metres of oil? Take g = 10 m/s² .

Concept:

The total Energy of fluid at any given point can be defined as the summation of Potential Energy, Pressure Energy, and Kinetic Energy at the same point.

\(E_{total} = E_{potential} + E_{pressure} + E_{kinetic}\)

Unit of Energy is generally taken as Joule. However, for ease of understanding and calculation, sometimes it is also expressed in terms of the head (meter) of fluid.

Total Energy formula in terms of head,

 \(E_{total} = {P \ \over \rho g} + Z + {V^2 \ \over 2 g} ~\)

Calculation:

Given:

Given data, at a given point, 

Pressure head  (\({P \ \over \rho g}\)) = 3 m of oil

Potential head (Z) = 4 m of oil

Oil Flow (Q) = 100 liter/s

We know, Velocity (V) = Oil Flow (Q) / Cross section Area (A)

Therefore \(V = {Q \ \over( \pi/4) \times d^2} = {100 \times10^{-3} \ \over \pi/4 \times0.3^2} = 1.41\) m/s

Velocity head \({V^2 \ \over 2 \times g} = {1.41^2 \ \over 2 \times 10} = 0.09\) m ~ 0.1 m

Therefore E_total = 3 + 4 + 0.1 = 7.1 m of oil