Question

What should be the diameter of an open well to give a safe yield of 4.8 l/s? Assume working head as 3.75 m and sub soil consists of fine sand of \( C = 0.5\ \text{h}^{-1} \).

• A. 1.50 m
• B. 2.25 m
• C. 3.04 m
• D. 4.20 m

Hint:

Use the formula \( Q = C \cdot h \cdot D^2 \) for estimating yield of open wells, where \( C \) depends on soil type (e.g., 0.5 for fine sand).

Answer 1

The Correct Option is C

The yield of an open well is given by the empirical formula: \[ Q = C \cdot h \cdot D^2 \] where:
- \( Q \) = discharge or safe yield in \( \text{litres/second} \),
- \( C \) = specific yield or well coefficient in \( \text{h}^{-1} \),
- \( h \) = working head in meters,
- \( D \) = diameter of the well in meters.
Given: \[ Q = 4.8\ \text{l/s},\quad h = 3.75\ \text{m},\quad C = 0.5\ \text{h}^{-1} \] Rewriting the formula to solve for \( D \): \[ D = \sqrt{\frac{Q}{C \cdot h}} = \sqrt{\frac{4.8}{0.5 \times 3.75}} = \sqrt{\frac{4.8}{1.875}} = \sqrt{2.56} = 1.6\ \text{m} \] But this is radius, so diameter is: \[ D = 2 \times 1.6 = 3.2\ \text{m} \] Given options, the closest correct diameter is: \[ \boxed{3.04\ \text{m}} \] Thus, the diameter of the open well should be 3.04 m.