Section 4: Soil and Water Conservation Engineering
Fluid Statics, Pressure & Manometry
Subtopic: Differential manometer deflection
Question Statement:
A differential mercury-water U-tube manometer connected across a pipeline carrying water registers a mercury column deflection of $25.0\text{ cm}$. Taking density of mercury as $13600\text{ kg/m}^3$ and water as $1000\text{ kg/m}^3$, the pressure head difference between the two points is ________ $\text{m of water}$ (round off to two decimal places).
Answer Key:
3.15
Step-by-Step Solution & Explanation
The pressure head difference $h$ across a differential manometer carrying a heavier manometric liquid is:
$h = y \left( \frac{S_m}{S} - 1 \right)$
where $y = 0.25\text{ m}$, $S_m = 13.6$, and $S = 1.0$.
$h = 0.25 \times (13.6 - 1) = 0.25 \times 12.6 = 3.150\text{ m of water}$
Rounding to two decimal places: $3.15\text{ m}$.