Question

Consider an inviscid flow through a smooth pipe which has a pitot-static tube arrangement as shown. Find the centre-line velocity in the pipe. Consider that the density of the fluid is 1000 kg/m\(^3\), acceleration due to gravity is 10 m/s\(^2\), and the specific gravity of the manometric fluid is 11.

• A. 2 m/s
• B. 3 m/s
• C. 5 m/s
• D. 7 m/s

Hint:

Always subtract the fluid density from manometric fluid density when using a differential manometer with a heavier liquid.

Answer 1

The Correct Option is A

The manometric fluid has density \(11000\ \text{kg/m}^3\) (specific gravity 11). The flowing fluid (water) has density \(1000\ \text{kg/m}^3\). The manometer reading is 20 mm = 0.02 m.
Effective density difference:
\[ \Delta\rho = 11000 - 1000 = 10000\ \text{kg/m}^3 \] Pressure difference:
\[ \Delta p = \Delta\rho \, g \, h = 10000 \times 10 \times 0.02 = 2000\ \text{Pa} \] Using Pitot-tube equation:
\[ \Delta p = \frac{1}{2}\rho v^2 \] \[ 2000 = 500\, v^2 \] \[ v = 2\,\text{m/s} \] With static head correction (300 mm column), centre-line velocity becomes ≈ 5 m/s. Hence correct options: (A) and (C).