Question

There is a small hole at the bottom of tank filled with water. If total pressure at the bottom is 3 atm(1 atm=10^(5)Nm^(-2)), then find the velocity of water flowing from hole.

Answer 1

The velocity of water flowing from the hole at the bottom of the tank is 20 m/s.

- It is given that :

Total pressure = 3 atm

Atmospheric pressure = 1 atm

⇒ Gauge pressure, P = (3 - 1) = 2 atm = 2 × 10⁵ Pa

- We know that P = hρg

⇒ gh = P/ρ

- We know  that, velocity of water flowing through hole is given  by

v = √(2gh) = √(2P/ρ)

v = √(2 × 2 × 10⁵) / 10³

v = √(4 × 10²)

v = √400 = 20 m/s

Answer 2

The velocity of water flowing from hole is :

•Given : Total pressure at bottom = 3 atm, 1 atm = 10^5 N/m^2

We know that,

• Change in pressure, ∆P

= 1/2×rho×v^2

Where rho = density of water

• v = √(2∆P/rho) = √2×(3-1)/rho

= √2×2×10^5/10^3

• v = √400 m/s

Therefore, velocity of water flowing from hole is √400 m/s