Question

Consider a tank of height 20m filled with liquid of density 100kg/m^3. The area of tank is 10m^2. If the tank has a hole of area 2m^2 at the bottom, find the speed of the liquid flowing out through the hole when the height of liquid in the tank is 10m . Assume speed of liquid descending at top of tank is 5m/s.

(a) 20m/s

(b) 14.14m/s

(c) 15m/s

(d) 20.615m/s

I got this question during an internship interview.

My doubt stems from Fluids Mechanical Properties in chapter Mechanical Properties of Fluids of Physics – Class 11

Answer 1

The correct option is (c) 15m/s

To explain: We can’t consider the speed of efflux to be \(\sqrt{2gh}\) as the areas are comparable. So, we use Bernoulli theorem between the top of the tank and the hole.                                                                                   Pressure at the top of tank and hole will be same, equal to P0,                                                                   since both are exposed to the atmosphere.

P0 + ρgH + 1/2ρ \(v_{1}^{2}\) = P0+ 1/2ρ\(v_{2}^{2}\)

∴  v2 = \(\sqrt{2(gh + v_{1}^{2}/2)}\)

= \(\sqrt{2(10 * 10 + 25/2)}\)

=  15m/s.