Question

A pipe of 100 mm diameter is suddenly stretched to a diameter of 200 mm. If the discharge is 60 L/s, then calculate the loss of energy per unit weight of water.
1. 2.0 m
2. 3.2 m
3. 1.5 m
4. 1.67 m

Answer 1

Correct Answer - Option 4 : 1.67 m

Concept:

Head loss due to sudden enlargement of pipe is given by,

\({\left( {{h_L}} \right)_{exp}} = \frac{{{{\left( {{v_1} - {v_2}} \right)}^2}}}{{2g}}\)

Where, v₁ is the velocity in smaller section and v₂ is the velocity in enlarged section 

Calculation:

Given, 

Q = 60 L/s = 0.06 m³/s

d₁ = 100 mm = 0.1 m,

\({A_1} = \frac{\pi }{4}d_1^2 = 0.00785\;{m^2}\)

d2 = 200 mm = 0.2 mm

\({A_2} = \frac{\pi }{4}d_2^2 = 0.0314\;{m^2}\)

\({v_1} = \frac{Q}{{{A_1}}} = \frac{{0.06}}{{0.00785}} = 7.643\;m/s\) 

\({v_2} = \frac{Q}{{{A_2}}} = \frac{{0.06}}{{0.0314}} = 1.91\;m/s\)

\({\left( {{h_L}} \right)_{exp}} = \frac{{{{\left( {{7.643} - {1.91}} \right)}^2}}}{{2\times 9.81}}=1.675\;m\)

Loss of energy per unit weight of water is given by 1.675 m