Fluid Mechanics | Surface Tension And Viscosity | JEE Main previous year questions with Solutions

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Q 1 :

A cylinder of height 20 m is completely filled with water. The velocity of efflux of water $({in ms}^{- 1})$ through a small hole on the side wall of the cylinder near its bottom is $(take g = 10 {m/s}^{2})$

(20)

$Given, Height of cylinder, h = 20 cm$

$Acceleration due to gravity, g = 10 {ms}^{- 2}$

$Velocity of efflux v = \sqrt{2 g h}$

$Where h is the height of the free surface of liquid from the hole$

$v = \sqrt{2 \times 10 \times 20} = 20 m/s$

Q 2 :

Water flows into a large tank with flat bottom at the rate of $10^{- 4} m^{3} s^{- 1}$ . Water is also leaking out of a hole of area $0.5 c m^{2}$ at its bottom. If the height of the water in the tank remains steady, then this height is $g = 10 m / s^{2}$

25 cm
15 cm
20 cm
5 cm

(3)

Since height of water column is constant therefore,

Water inflow rate $(Q_{m})$ = water outflow rate

$Q_{i n} = 10^{- 4} m^{3} s^{- 1}$

$Q_{o u t} = A u = 10^{- 4} \times \sqrt{2 g h}$

$10^{- 4} = 10^{- 4} \sqrt{20 \times h}$

$h = \frac{1}{20} m = 5 c m$

Topic Question Set

Q 1 :

A cylinder of height 20 m is completely filled with water. The velocity of efflux of water $({in ms}^{- 1})$ through a small hole on the side wall of the cylinder near its bottom is $(take g = 10 {m/s}^{2})$

Q 2 :

Water flows into a large tank with flat bottom at the rate of $10^{- 4} m^{3} s^{- 1}$ . Water is also leaking out of a hole of area $0.5 c m^{2}$ at its bottom. If the height of the water in the tank remains steady, then this height is $g = 10 m / s^{2}$

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Topic Question Set

Q 1 : A cylinder of height 20 m is completely filled with water. The velocity of efflux of water (in ms-1) through a small hole on the side wall of the cylinder near its bottom is (take g=10 m/s2)

Q 2 : Water flows into a large tank with flat bottom at the rate of 10-4m3s-1. Water is also leaking out of a hole of area 0.5cm2 at its bottom. If the height of the water in the tank remains steady, then this height is g=10m/s2

Want Us to Email you About Special Offers & Updates?

Q 1 :

A cylinder of height 20 m is completely filled with water. The velocity of efflux of water $({in ms}^{- 1})$ through a small hole on the side wall of the cylinder near its bottom is $(take g = 10 {m/s}^{2})$

Q 2 :

Water flows into a large tank with flat bottom at the rate of $10^{- 4} m^{3} s^{- 1}$ . Water is also leaking out of a hole of area $0.5 c m^{2}$ at its bottom. If the height of the water in the tank remains steady, then this height is $g = 10 m / s^{2}$