Question

A U-tube manometer with a small quantity of mercury is used to measure the static pressure difference between two locations A and B in a conical section through which an incompressible fluid flows. At a particular flow rate, the mercury column appears as shown in the figure. The density of mercury is 13600 kg/$m^3$ and g = 9.81 $m/s^2$. Which of the following is correct?

• A. Flow direction is A to B and $p_A-p_B=20kPa$
• B. Flow direction is B to A and $p_A-p_B=1.4kPa$
• C. Flow direction is A to B and $p_B-p_A=20kPa$
• D. Flow direction is B to A and $p_B-p_A=1.4kPa$

Answer 1

The correct option is A Flow direction is A to B and $p_A-p_B=20kPa$

Flow direction is A to B because pressure at section A is more than at section B.

$p_{{}_A}-p_{{}_B}=(\rho gh{)}_{Hg}={\rho }_{{}_{Hg}}g{h}_{Hg}$
where,
${\rho }_{{}_{Hg}}=13600kg/m^3$
$g=9.81m/s^2$
$h_{Hg}=150mm=0.15m$
$\therefore p_{{}_A}-p_{{}_B}=13600\times 9.81\times 0.15$
=20012.4 Pa = 20.01 kPa