Question

A U tube is made of two capillary tubes of diameter 0.5 mm There are two identical small holes on the opposite sides of a tank containing a liquid. The tank is open at the top. The difference in height between the two holes is h. As the liquid comes out of the two holes, the tank will experience a net horizontal force proportional to

• A. √h
• B. h
• C. h^3/2
• D. h²

Answer 1

Answer: (B)

h

Answer 2

v₁ = $\sqrt { 2 g x }$

Let ρ = density of the liquid.

Let α = area of cross – section of each hole.

Volume of liquid discharged per second at a hole

= αv (v = v₁ or v₂)

Mass of liquid discharged per second = αvρ.

Momentum of liquid discharged per second = αv²ρ.

$\Rightarrow$The force exerted at the upper hole (to the right) = αρv₂²

and the force exerted at the lower hole (to the left) = αρv₁².

Net fore on the tank = αρ[v₁² – v₂²] = αρ[2g(h + x) – 2gx]

= 2αρgh.