fluid mechanics Water flows from a reservoir tank which is o

fluid mechanics

Water flows from a reservoir tank which is open to the air and is 80 ft above the exit through a galvanized iron pipe which has a diameter of 2 inches. There are minor losses at the entrance of the pipe (K = 0.5) and two 90 degree bends (K = 0.9) pipe. The total pipe length is 100 ft. Determine the head loss in the pipe and flow-rate Q.

Solution

Using Bernoullis eqn for flow through a tube,

p1 + 1/2 x rho x v^2 = zero at \'h = 0\' -------------- eqn 1

a) The difference in height of the reservoir and the pipe creates a pressure head given by,

p1 - p2 = rho x g x (h2 - h1)

Also apply eqn 1 to the flow at the throat of the reservoir and pipe,

p1 = p2 + 1/2 x rho x v^2

p1 - p2 = 1/2 x rho x v^2

rho x g x (H2 - (H1 + H loss)) = 1/2 x rho x v^2 -------- (1)

Hloss = k x L/D x v^2 / 2g

replacing with the values,

Hloss = (0.5+0.9) x 100 x v^2 / 2 x32.18= 2.17v^2 ----- (2)

Replae with values in (1) above,

g (H2 - (H1 + 2.17v^2)) = 0.5 v^2 where H1 = 0 and g = 32.18 ft/s2

32.18 (80 - 2.17 v^2) = 0.5v^2

v^2 = 2574.4 / 70.33 = 36.6

v = 6.05 ft/s

b) Flow rate dot m or Q = rho x A x V

Q = (62.43/32.18) x 3.14 x 0.0069 x 6.05 = 0.25 ft /s^2