Chapter 10, Problem 10.1PP

Determine the energy loss due to a sudden enlargement from a $50$ mm $ODx2.4$ mm wall plastic pipe to a $90$ mm $ODx2.8$ mm wall plastic pipe when the velocity of flow is $3$ m/s in the smaller pipe.

To determine

The energy loss due to sudden enlargement.

Answer to Problem 10.1PP

The energy loss due to sudden enlargement in terms of head is $h_l=0.233\text{}\text{m}$.

Explanation of Solution

Given information:

For pipe 1:

Outer Diameter D = 50 mm

Pipe wall thickness t₁= 2.4 mm

Thus, Inner diameter of the pipe 1 = D − 2t = 45.2 mm

The velocity of flow v₁= 3 m/s

For pipe 2:

Outer Diameter D = 90 mm

Pipe wall thickness t₂= 2.8 mm

Thus, Inner diameter of the pipe 2 = D − 2t = 84.4 mm

Calculation:

The energy loss due to sudden enlargement is given in terms of head lost. The formula for head loss due to sudden expansion is given by:

   $h_l=\frac{V_1{}^2}{2\times g}{\left(1-{\left(\frac{d_1}{d_2}\right)}^2\right)}^2$          ...... (1)

Putting given values in equation (1)

   $h_l=\frac{3^2}{2\times 9.81}{\left(1-{\left(\frac{45.2\times {10}^{-3}}{84.4\times {10}^{-3}}\right)}^2\right)}^2$

   $h_l=0.233\text{}\text{m}$

Conclusion:

Thus, the energy loss due to sudden enlargement in terms of head is $h_l=0.233\text{}\text{m}$.