Question

A U-tube acts as a water siphon. The bend in the tube is $1m$ above the water surface. The tube outlet is $7m$ below the water surface. The water issues from the bottom of the siphon as a free jet at atmospheric pressure. Speed of jet is $v$ and minimum absolute pressure in the bend is $p$. (Given $p_{atm}=1.01\times {10}^{8}N{m}^{-2},g=9.8m{s}^{-2};{\rho }_{water}=1000kg{m}^{-3}$)

• A. $v=11.7m{s}^{-1}$
• B. $v=13.2m{s}^{-1}$
• C. $p=2.27\times {10}^{4}N{m}^{-2}$
• D. $p=3.27\times {10}^{4}N{m}^{-2}$

Answer 1

The correct option is A $v=11.7m{s}^{-1}$

Applying Bernoulli's equation between both points.

$p_1+\frac{1}{2}\rho v_1^2+\rho g{h}_1=p_2+\frac{1}{2}\rho v_2^2+\rho g{h}_2$

$v_1\approx 0$

also, p1=p2=atmospheric pressure

$\rho g{h}_1=\frac{1}{2}\rho v_2^2+\rho g{h}_2$

$\rho g(h_1-h_2)=\frac{1}{2}\rho v_2^2$

$v_2^2=2g(h_1-h_2)$

$v_2=\sqrt{2\times 9.8\times 7}$

$v_2=11.7m/s$

so option 'A' is correct.