Question

In a horizontal pipeline a 150 mm diameter pipe is connected to a 250 mm diameter pipe. The flow rate in the pipeline is 0.15 m^3/s. Take the connection as a sudden enlargement and determine: (a) The pressure head loss vhen the vater flovs from the large pipe to the smaller pipe (take Cc=0.64) (b) The pressure head loss when vater flovs from the small pipe to the larger pipe (c) The loss of power in both cases

Answer 1

a)
`h_L=1.17m`

b)
`h_L=1.52m`

c)
`P_1=1.721 kN`

`P_2=2.236 kN`

Step-by-step explanation:

velocities of the pipe;

velocity of small dia pipe

`v_(small)=(Q)/(A_(small)) =(0.15)/((\pi)/(4)* d^2 )= (0.15)/((\pi)/(4)* 0.15^2 )=8.52m/s`

velocity of larger dia pipe

`v_(large)=(Q)/(A_(large)) =(0.15)/((\pi)/(4)* d^2 )= (0.15)/((\pi)/(4)* 0.25^2 )=3.05m/s`

a) pressure head loss when water is flowing from large to smaller pipe

`h_L=((1)/(C_c) -1)^2 * (v^2)/(2g)`

`h_L=((1)/(0.64) -1)^2 * (8.52^2)/(2* 9.81) = 1.17m`

b) pressure head loss when water flow from small pipe to large pipe

`h_L= (v^2)/(2g)(1-(A_(small))/(A_(large)) )^2`

`h_L=(8.52^2)/(2*9.81)(1-((\pi)/(4)* 0.15^2)/((\pi)/(4)* 0.25^2)} )^2= 1.52 m`

c) power loss in both cases are

`P_1= \rho g Q h_(L1)= 1000 * 9.81* 0.15* 1.17= 1.721 kN`

`P_2= \rho g Q h_(L2)= 1000 * 9.81* 0.15* 1.52= 2.236 kN`