Question

Water flows through the tube shown Area of cross-section of wide and narrow part are $5{cm}^2$ & $2{cm}^2$ . The rate of flow is 500 ${cm}^3/sec$ Find difference mercury level of U-tube:

• A. 2.9 cm
• B. 1.97 cm
• C. 0.9 cm
• D. None of these

Answer 1

The correct option is B 1.97 cm

$V_1=\frac{500}{5}=100cm/s$

and $V_2=\frac{500}{2}=250cm/s$

Now$,$ using bernoulii's equation

$P_1+\frac{1}{2}\rho {V_1}^2=P_2+\frac{1}{2}\rho {V_2}^2$

or$,$ $P_1-P_2=\frac{1}{2}\rho {V_2}^2-\frac{1}{2}\rho {V_1}^2$

Thus$,$ in the given case pressure difference $=\frac{1}{2}\times 1\left(625\times {10}^2-100\times {10}^2\right)$

Now$,$

$h\times 13.6\times 980=50\times 625$

or$,$ $h=1.97cm$

Hence,

option $\left(B\right)$ is correct answer.