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