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

Q 11 :

The surface of water in a water tank of cross-sectional area $750 {cm}^{2}$ on the top of a house is $h$ m above the tap level. The speed of water coming out through the tap of cross-sectional area $500 {mm}^{2}$ is $30 cm/s$ . At that instant, $\frac{d h}{d t}$ is $x \times 10^{- 3} m/s$ . The value of $x$ will be _______. [2023]

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(2)

$a_{1} v_{1} = a_{2} v_{2}$

$750 \times 10^{- 4} v_{1} = 500 \times 10^{- 6} \times 0.3$

$v_{1} = \frac{500 \times 3 \times 10^{- 3}}{750} m/s = 2 \times 10^{- 3} m/s$

$\Rightarrow \frac{d h}{d t} = - 2 \times 10^{- 3} m/s$

Q 12 :

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 fluid is _________ ${cm s}^{- 1}$ . [2023]

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(80)

$By equation of continuity$

$A_{1} V_{1} = A_{2} V_{2}$

$\Rightarrow V_{2} = \frac{2 \times 4}{10 \times 10^{- 2}} = 80 cm/s$

Q 13 :

Glycerine of density $1.25 \times 10^{3} {kg m}^{- 3}$ is flowing through the conical section of a pipe. The area of cross-section of the pipe at its ends is $10 {cm}^{2}$ and $5 {cm}^{2}$ and the pressure drop across its length is ${3 N m}^{- 2}$ . The rate of flow of glycerine through the pipe is $x \times 10^{- 5} m^{3} s^{- 1}$ . The value of $x$ is _________. [2023]

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(4)

$Δ P = P_{1} - P_{2} = {3 N/m}^{2} (given)$

${By continuity eq}^{n}, A_{1} v_{1} = A_{2} v_{2}$

$∴$ $v_{1} = \frac{A_{2}}{A_{1}} v_{2}$ ...(i)

${By Bernoulli's eq}^{n},$

$P_{1} + \frac{1}{2} ρ v_{1}^{2} = P_{2} + \frac{1}{2} ρ v_{2}^{2}$

$P_{1} - P_{2} = \frac{1}{2} ρ (v_{2}^{2} - v_{1}^{2})$

$\Rightarrow Δ P = \frac{1}{2} ρ [1 - {(\frac{A_{2}}{A_{1}})}^{2}] v_{2}^{2}$

$3 = \frac{1}{2} \times 1.25 \times 10^{3} [1 - {(\frac{5}{10})}^{2}] v_{2}^{2}$

$∴$ $v_{2} = 8 \times 10^{- 2} m/s$

$So discharge rate = A_{2} v_{2} = 5 \times 10^{- 4} \times 8 \times 10^{- 2} = 4 \times 10^{- 5} m^{3} / s$

$Correct answer is x = 4$

Q 14 :

Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of cross-sections at A and B are $6 {cm}^{2}$ and $3 {cm}^{2}$ respectively. The rate of flow will be ______ ${cm}^{3} / s$ . (take g = 10 m/s²) [2026]

$\frac{200}{\sqrt{3}}$
$100 \sqrt{3}$
$200 \sqrt{3}$
$200 \sqrt{6}$

1

2

3

4

(3)

From continuity equation

$A_{A} V_{A} = A_{B} V_{B} \Rightarrow 6 V_{A} = 3 V_{B} \Rightarrow V_{B} = 2 V_{A}$

Applying Bernoulli's equation between A & B,

$P_{A} + \frac{1}{2} ρ V_{A}^{2} = P_{B} + \frac{1}{2} ρ V_{B}^{2}$

$\Rightarrow ρ g \times 0.05 = \frac{1}{2} ρ [V_{B}^{2} - V_{A}^{2}] = \frac{1}{2} ρ (3 V_{A}^{2})$

$\Rightarrow V_{A} = \sqrt{\frac{2 g \times 0.05}{3}} m/s = \frac{1}{\sqrt{3}} m/s = \frac{100}{\sqrt{3}} cm/s$

$\Rightarrow Volume flow rate = A_{A} V_{A} = \frac{6 \times 100}{\sqrt{3}} {cm}^{3} / sec$

$= 200 \sqrt{3} {cm}^{3} / sec$

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Topic Question Set

Q 11 : The surface of water in a water tank of cross-sectional area 750 cm2 on the top of a house is h m above the tap level. The speed of water coming out through the tap of cross-sectional area 500 mm2 is 30 cm/s. At that instant, dhdt is x×10-3 m/s. The value of x will be _______. [2023]

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Q 12 : Figure below shows a liquid being pushed out of the tube by a piston having area of cross section 2.0 cm2. The area of cross section at the outlet is 10 mm2. If the piston is pushed at a speed of 4 cm s-1, the speed of outgoing fluid is _________ cm s-1. [2023]

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Q 14 : Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of cross-sections at A and B are 6cm2 and 3cm2 respectively. The rate of flow will be ______ cm3/s. (take g = 10 m/s²) [2026]

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