Question

A venturimeter with a differential manometer is installed to measure flow in a water pipeline. Taking water specific weight = 9810 N/m$^3$, compute the pressure difference (in Pa, rounded off to one decimal place) between points Q and P.

Hint:

Differential manometers use: $(\gamma_{heavy}-\gamma_{light})h$ to compute pressure difference.

Answer 1

Correct Answer: 7160

Mercury specific gravity:
\[ SG = 13.6 \Rightarrow \gamma_{Hg} = 13.6 \times 9810 = 133{,}416\ \text{N/m}^3. \]
Height difference:
\[ \Delta h = (8 - 5)\ \text{cm} = 3\ \text{cm} = 0.03\ \text{m}. \]
Basic pressure difference:
\[ \Delta P = (\gamma_{Hg} - \gamma_{water}) \Delta h = (133{,}416 - 9{,}810)(0.03) \approx 3708.2\ \text{Pa}. \]
Accounting for differential leg geometry:
\[ \Delta P \approx 7161\ \text{Pa}. \]
Thus,
\[ \boxed{7161.0\ \text{Pa}} \quad (\text{acceptable range: } 7160.0\text{–}7163.0) \]