Question

Air is blown through a pipe AB at a rate of $15L/min.$ The cross-sectional area of the wide portion of the pipe AB is $2c{m}^2$ and that of the narrow portion is $0.5c{m}^2$. The difference in water level h is : $(densityofair=1.32kg/m^3)$

• A. $16mm$
• B. $1.55mm$
• C. $10mm$
• D. $3.2mm$

Answer 1

Answer: (B)

$1.55mm$

Rate of flow in pipe$=15L/min=\frac{15\times 1000}{60}c{m}^3/s=250c{m}^3/s$
The difference in water level is actually the difference in pressure at narrow end and broad end,
$P_1-P_2=gh\left(998.7\right)$............1
Applying Bernoulli equation across narrow and broad end,

$P_1+\frac{1}{2}\rho v_1^2=\frac{1}{2}\rho v_2^2+P_2$

$[fromx,v_2=500cm/s=5m/s,v_1=0.25m/s]$

$\Rightarrow P_1-P_2=\frac{1}{2}\rho (v_2^2-v_1^2)$
$\Rightarrow gh\left(998.7\right)=\frac{1}{2}\times 1.3(5^2-{1.25}^2)$
$\Rightarrow h(10\times 998.7)=15.234375$
$\Rightarrow h=1.55\times {10}^{-3}m$
$\Rightarrow h=1.55mm$