Water is flowing through a pipe of diameter 5cm under a pressure of 29.43N/cm2 (gauge) and with mean velocity of 2 m/s. Find the total energy per unit weight of the water at a cross-section, which is 5m above the datum line.

Water is flowing through a pipe of diameter 5cm under a pressure of 29.43N/cm2 (gauge) and with mean velocity of 2 m/s. Find the total energy per unit weight of the water at a cross-section, which is 5m above the datum line.

Solution

 Diameter of pipe = 5cm = 0.5 m

 Pressure p = 29.43N/cm2 = 29.43 x 104 N/m2

Datum head z =5m

Total head = pressure head + kinetic head+ datum head

Pressure head= p/ρg=29.43 x 104 /1000 x9.81 =30m

Kinetic head=v 2 /2g = 2x2/2x9.81= 0.204m

Total head= p/ρ g+ v2 /2g+z = 30+0.204+5 = 35.204 m