Question

can somebody help me with problem 4 please

3. A fluid of viscosity 5 Pa s and density 1,025 kg/m' is being pumped through a cast iron pipe (€ = 259 x 10m) of length 14 m and diameter 8 cm at the rate of 4 kg/s. What is the power required for this? 4. In the above problem, calculate the power requirement if three gate valves (1/4 closed), four globe valves (fully open), and two regular 45 threaded elbows are added to the system.

Answer 1

Mass flow rate m = 4kg/s

Rho*A*v = 4 kg/s

Density rho = 1025 kg/m3

Diameter of pipe d = 8 cm = 0.08 m

(1025 kg/m3)*π/4 * d² *v = 4 kg/s

1025*0.785*0.08²*v = 4

v = 0.77 m/s

Friction factor f = e/d = 2.59*10^-4m/0.08m = 0.0032

Head due to friction, hf = f*(L/d)*v²/2g = 0.0032*(14/0.08)*0.77²/2*9.8 = 0.016 m

By k factor table:

Gate valves K factor = 24

Three gate valves (1/4 closed) = 3*24 = 72

Globe valves (fully open) K factor = 6

Two regular threaded elbows K factor = 2*0.2 = 0.4

Overall K factor = 72 + 6 +0.4 = 78.4

Mass flow rate m = 4 kg/s

Head due to K factor hL = K*v²/2g = 78.4*0.77²/2*9.8 = 2.41m

Power requirement due to friction and fittings,

H = hL + hf = 2.41 + 0.016 =

P = m*g*(H) = 4 kg/s * 9.8 m/s2 * 2.426 m = 95.09 W

Power requirement P = 95.09 W