Water is flowing through a pipe of 6 cm diameter under a pressure of 200 × 10³ N/m² and with mean velocity of 2.0 m/s. Find the total head or total energy per unit weight of the water at a cross section which is 6 m above the datum line.

Concept:

Bernoulli's Equation:

" In an ideal incompressible fluid when the flow is steady and continuous, the sum of pressure energy, kinetic energy, and potential(or datum) energy is constant along a streamline." 

\({P\over ρ g}+{v^2\over 2g}+z=Constant\)

where \({P\over ρ g}=Pressure\, head\)

\({v^2\over 2g}=Kinetic\, head\)

z = Head from datum line

ρ = Density of fluid

g = Acceleration due to gravity

v = velocity of the fluid

Calculation:

Given data:

Diameter of pipe (D) = 6 cm

Pressure (P) = 200 × 10³ N/m²

Mean velocity (v) = 2.0 m/s

Total head or total energy per unit weight (H) =?

\(Total\, head(H)={P\over ρ g}+{v^2\over 2g}+z\)

\(Total\, head(H)={200\times 10^3\over 1000\times 9.81}+{2^2\over 2\times 9.81}+6\)

\(Total\, head(H)=20.387+0.203+6=26.59\, m\)

\(Total\, head(H)=26.59\, m\)

Total head or total energy per unit weight (H) = 26.59 m