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

Answer:

a) $h_L=1.17m$

b)$h_L=1.52m$

c)$P_1=1.721 kN$

  $P_2=2.236 kN$

Explanation:

velocities of the pipe;

velocity of small dia pipe

$v_{small}=\frac{Q}{A_{small}} =\frac{0.15}{\frac{\pi}{4}\times d^2 }= \frac{0.15}{\frac{\pi}{4}\times 0.15^2 }=8.52m/s$

velocity of larger dia pipe

$v_{large}=\frac{Q}{A_{large}} =\frac{0.15}{\frac{\pi}{4}\times d^2 }= \frac{0.15}{\frac{\pi}{4}\times 0.25^2 }=3.05m/s$

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

  $h_L=(\frac{1}{C_c} -1)^2 \times \frac{v^2}{2g}$

$h_L=(\frac{1}{0.64} -1)^2 \times \frac{8.52^2}{2\times 9.81} = 1.17m$

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

$h_L= \frac{v^2}{2g}(1-\frac{A_{small}}{A_{large}} )^2$

$h_L=\frac{8.52^2}{2\times9.81}(1-\frac{\frac{\pi}{4}\times 0.15^2}{\frac{\pi}{4}\times 0.25^2}} )^2= 1.52 m$

c) power loss in both cases are

$P_1= \rho g Q h_{L1}= 1000 \times 9.81\times 0.15\times 1.17= 1.721 kN$

$P_2= \rho g Q h_{L2}= 1000 \times 9.81\times 0.15\times 1.52= 2.236 kN$