A horizontal pipeline AB of diameter d conveys water, flowing from A to B. The U-tube manometer with mercury as manometric liquid can be used for the measurement of :
Try it first: pick an option, then read the explanation.
Asked in SSC JE 23.03.2021 (Morning Shift)
Detailed Explanation
When water flows through a pipe of uniform diameter, friction causes a continuous loss of pressure head along the direction of flow. Connecting a differential manometer across points A and B records this loss.
1. Analyze flow in a horizontal pipe of constant diameter \(d\):
- Pipe is horizontal: \(z_A = z_B\) (identical potential energy).
- Uniform cross-section: By continuity (\(A_A V_A = A_B V_B\)), velocities are identical: \(V_A = V_B\).
- Kinetic head is identical: \(\frac{V_A^2}{2g} = \frac{V_B^2}{2g}\).
2. Differential manometer reading \(x\) connects points \(A\) and \(B\):
\[ \frac{p_A - p_B}{\gamma_w} = x \left(\frac{S_m}{S_w} - 1\right) = x \left(\frac{13.6}{1.0} - 1\right) = 12.6 \, x \]
3. This quantity represents the difference in pressure head between points \(A\) and \(B\).
Why “difference in the pressure head between two points A and B” Is Correct
The differential manometer senses static fluid pressure at points A and B. Because elevation and diameter are identical along horizontal pipe AB, the manometric reading translates directly to the difference in pressure head (\(h_f = (p_A - p_B)/\gamma\)).
Why the Other Options Are Wrong
- A. difference in the total energy between two points A and B: Total energy includes kinetic, datum, and pressure heads; the manometer measures only piezometric pressure head.
- C. difference in the velocity between the points A and B: Velocity difference is zero in a uniform diameter pipe by the continuity equation.
- D. difference in the kinetic head at the two points A and B: Kinetic head difference is zero because velocity is unchanged between A and B.
Key Point
Differential manometer on horizontal uniform pipe measures difference in pressure head: Δh = (p_A − p_B)/γ.
Key Concepts for Students
- In a horizontal uniform pipe, head loss due to friction equals the difference in pressure head.
- For mercury and water: Δh = 12.6 · x, where x is the mercury deflection in the manometer.
- If the pipe was inclined, the manometer would measure difference in piezometric head: (p/γ + z)_A − (p/γ + z)_B.
Practice more: this is question 6 in Measurement of Pressure MCQs – Part 1. Try the whole set and check every answer instantly.