Question

In the experimental arrangement shown in figure, the areas of cross-section of the wide and narrow portions of the tube are 5 cm${}^2$ and 2 cm${}^2$ respectively. The rate of flow of water through the tube is 500 cm${}^3$ s${}^{-1}$. The difference of mercury levels in the U-tube is:

• A. $0.97cm$
• B. $1.97cm$
• C. $0.67cm$
• D. $4.67cm$

Answer 1

Answer: (B)

$1.97cm$

$Q=500c{m}^3/s$
Using continuity equation we have $Q=A_1{v}_1=A_2{v}_2$
or
$500=5\left(v_1\right)=2\left(v_2\right)$
Thus we get
$v_1=100cm/s=1m/s$ and $v_2=250cm/s=2.5m/s$

Applying Bernoullis therom, In point (1) and (2),
$\Rightarrow P_1-P_2=\frac{1}{2}\rho (v_2^2-v_1^2)=\frac{1}{2}1000({2.5}^2-1^2)=2625N/m^2$
$\Rightarrow P_1-P_2=2625=\rho gh=13.6\times 1000\times 9.8\times h$
$\Rightarrow h=1.97cm$