Question

If V is the mean velocity of flow, then according to Darcy-Weisbach equation for pipe flow energy loss over a length of pipeline is proportional to
1. V
2. 1/V
3. 1/V²
4. V²

Answer 1

Correct Answer - Option 4 : V²

Explanation:

Darcy Weisbach Equation for friction losses in circular pipe:

\({h_f} = \frac{{f \times L \times {V^2}}}{{2 \times g \times D}}\) or \({h_f}\; = \;\frac{{fL{Q^2}}}{{12.1{d^5}}}\)

where L = length of the pipe, D = diameter of the circular pipe, V = mean velocity of the flow, f = Darcy’s friction factor = 4 × F’, F’ = coefficient of friction and hf = head loss due to friction

The energy loss over a length of the pipeline is \(\frac{h_f}{L} = \frac{{f \times {V^2}}}{{2 \times g \times D}}\)

Here f, g, and for a pipe D remains constant \(\therefore \frac{h_f}{L}\propto{V^2}\)

The energy loss over the length of the pipeline is proportional to V².