JEE Advanced · 2014 · 25 May 2014 · Paper 2 · Fluid Mechanics

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A spray gun is shown in the figure where a piston pushes air out of a nozzle. A thin tube of uniform cross section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid from the container rises into the nozzle and is sprayed out. For the spray gun shown, the radii of the piston and the nozzle are

20 mm

and

1 mm

, respectively. The upper end of the container is open to the atmosphere.

If the piston is pushed at a speed of

5 mm s^{- 1}

, the air comes out of the nozzle with a speed of

(A) $0.1 m s^{- 1}$
(B) $1 m s^{- 1}$
(C) $2 m s^{- 1}$ ✓ Correct
(D) $8 m s^{- 1}$

Answer: (C)

Solution

Using the continuity equation for incompressible flow:

A_{1} v_{1} = A_{2} v_{2}

.

For the piston:

A_{1} = π (20)^{2}

v_{1} = 5

mm/s.

For the nozzle:

A_{2} = π (1)^{2}

v_{2} = ?

π (20)^{2} \times 5 = π (1)^{2} \times v_{2}

v_{2} = \frac{400 \times 5}{1} = 2000

mm/s =

2

m/s.

JEE Advanced · 2014 · 25 May 2014 · Paper 2 · Single correct option

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JEE Advanced · 2014 · 25 May 2014 · Paper 2 · Fluid Mechanics

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