Figure below shows a liquid being pushed out of the tube by a piston having area of cross section $2.0 \mathrm{~cm}^{2}$. The area of cross section at the outlet is $10 \mathrm{~mm}^{2}$. If the piston is pushed at a speed of $4 \mathrm{~cm} \mathrm{~s}^{-1}$, the speed of outgoing fluidis \_\_\_\_ $\mathrm{cm} \mathrm{~s}^{-1}$.

JEE Main · 2023 · 10 Apr 2023 · Shift 2 · Fluid Mechanics

Figure below shows a liquid being pushed out of the tube by a piston having area of cross section

2.0 cm^{2}

. The area of cross section at the outlet is

10 mm^{2}

. If the piston is pushed at a speed of

4 cm s^{- 1}

, the speed of outgoing fluidis ____

cm s^{- 1}

Answer: 80

Solution

By the equation of continuity,

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

. Here,

A_{1} = 2.0

cm²,

v_{1} = 4

cm/s, and

A_{2} = 10

mm²

= 0.1

cm². Therefore,

v_{2} = \frac{A _{1} v _{1}}{A _{2}} = \frac{2.0 \times 4}{0.1} = 80

cm/s.

JEE Main · 2023 · 10 Apr 2023 · Shift 2 · Integer answer

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