Consider a cylindrical tank of radius 1 m is filled with water. The top surface of water is at 15 m from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of 5 m from the bottom. A force of 5 × 105 N is applied an the top surface of water using a piston. The speed of efflux from the hole will be: (given atmospheric pressure P A =1.01 × 105 Pa, density of water ρ w =1000 kg / m 3 and gravitational acceleration g=10 m / s 2 )

Question

Consider a cylindrical tank of radius 1 m is filled with water. The top surface of water is at 15 m from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of 5 m from the bottom. A force of 5 × 105 N is applied an the top surface of water using a piston. The speed of efflux from the hole will be: (given atmospheric pressure P A =1.01 × 105 Pa, density of water ρ w =1000 kg / m 3 and gravitational acceleration g=10 m / s 2 ) (A) 11.6 m / s (B) 10.8 m / s (C) 17.8 m / s (D) 14.4 m / s

Tardigrade Admin · Accepted Answer

Apply Bernoulli's theorem between Piston and hole

P_{A} + ρ g h = P_{0} + \frac{1}{2} ρ v_{e}^{2}

Assuming there is no atmospheric pressure on piston

\frac{5 \times 1 0 ^{5}}{π} + 1 0^{3} \times 10 \times 10 = 1.01 \times 1 0^{5} + \frac{1}{2} \times 1 0^{3} \times v_{e}^{2}

v_{e} = 17.8 m / s

$11.6 m / s$

$10.8 m / s$

$17.8 m / s$

$14.4 m / s$

11.6m/s

10.8m/s

17.8m/s

14.4m/s

Apply Bernoulli's theorem between Piston and hole PA​+ρgh=P0​+21​ρve2​ Assuming there is no atmospheric pressure on piston π5×105​+103×10×10=1.01×105+21​×103×ve2​ ve​=17.8m/s

$11.6 m / s$

$10.8 m / s$

$17.8 m / s$

$14.4 m / s$