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

Q 1 :
Correct Bernoulli's equation is (symbols have their usual meaning) [2024]

$P + ρ g h + \frac{1}{2} ρ v^{2} = c o n s \tan t$
$P + ρ g h + ρ v^{2} = c o n s \tan t$
$P + m g h + \frac{1}{2} m v^{2} = c o n s \tan t$
$P + \frac{1}{2} ρ g h + \frac{1}{2} ρ v^{2} = c o n s \tan t$

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(A) $P + ρ g h + \frac{1}{2} ρ v^{2} = c o n s \tan t$

Energy per unit volume is conserved.

Q 2 :
The reading of pressure metre attached with a closed pipe is $4.5 \times 10^{4} N / m^{2}$ . On opening the valve, water starts flowing and the reading of pressure metre falls to $2.0 \times 10^{4} N / m^{2}$ . The velocity of water is found to be $\sqrt{V} m / s$ . The value of V is ___________ . [2024]

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(50) $Change in pressure = \frac{1}{2} ρ v^{2}$

$4.5 \times 10^{4} - 2 \times 10^{4} = \frac{1}{2} \times 10^{3} \times v^{2}$

$2.5 \times 10^{4} = \frac{1}{2} \times 10^{3} \times v^{2}$

$v^{2} = 50$

$v = \sqrt{50}$

Q 3 :
A plane is in level flight at constant speed and each of its two wings has an area of $40$ $m^{2}$ . If the speed of the air is 180 km/h over the lower wing surface and 252 km/h over the upper wing surface, the mass of the plane is __________ kg.

$(T a k e a i r d e n s i t y t o b e 1 k g$ $m^{- 3}$ $a n d$ $g = 10$ $m s^{- 2})$ [2024]

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(9600) By Bernoulli's equation

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

$\frac{1}{2} \times ρ \times [4900 - 2500] = \frac{m g}{A}$

$\frac{1}{2} \times 1 \times 2400 = \frac{m \times 10}{80}$

$m = 9600 kg$

Q 4 :
Given below are two statements:

Statement I: When speed of liquid is zero everywhere, pressure difference at any two points depends on equation $P_{1} - P_{2} = ρ g (h_{2} - h_{1}) .$

Statement II: In venturi tube shown, $2 g h = v_{1}^{2} - v_{2}^{2}$

In the light of the above statements, choose the most appropriate answer from the options given below. [2024]

Both Statement I and Statement II are correct.
Both Statement I and Statement II are incorrect.
Statement I is correct but Statement II is incorrect.
Statement I is incorrect but Statement II is correct.

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(3)

From Bernoulli’s equation

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

[ $h_{1}$ and $h_{2}$ are height of points from any reference level]

For statement 1:

When speed of liquid is zero everywhere, $v_{1} = v_{2} = 0$

$∴$ $P_{1} - P_{2} = ρ g (h_{2} - h_{1}),$ Hence, statement I is correct.

For statement 2, $h_{1} = h_{2}$

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

But, $P_{1} - P_{2} = ρ g h \Rightarrow ρ g h = \frac{1}{2} ρ (v_{2}^{2} - v_{1}^{2})$

Hence, $2 g h = v_{2}^{2} - v_{1}^{2}$ , Hence statement II is incorrect.

Q 5 :
In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wings are 70 ${ms}^{- 1}$ and 65 ${ms}^{- 1}$ respectively. If the wing area is 2 $m^{2}$ the lift of the wing is ______ N.

(Given density of air = 1.2 kg $m^{- 1}$ ) [2024]

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(810)

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

$F = \frac{1}{2} \times 1.2 \times (70^{2} - 65^{2}) \times 2 = 810 N$

Topic Question Set

Q 1 :
Correct Bernoulli's equation is (symbols have their usual meaning) [2024]

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Q 5 :
In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wings are 70 ${ms}^{- 1}$ and 65 ${ms}^{- 1}$ respectively. If the wing area is 2 $m^{2}$ the lift of the wing is ______ N.

(Given density of air = 1.2 kg $m^{- 1}$ ) [2024]

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Topic Question Set

Q 1 : Correct Bernoulli's equation is (symbols have their usual meaning) [2024]

Q 2 : The reading of pressure metre attached with a closed pipe is 4.5×104N/m2. On opening the valve, water starts flowing and the reading of pressure metre falls to 2.0×104N/m2. The velocity of water is found to be Vm/s. The value of V is ___________ . [2024]

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Q 3 : A plane is in level flight at constant speed and each of its two wings has an area of 40 m2. If the speed of the air is 180 km/h over the lower wing surface and 252 km/h over the upper wing surface, the mass of the plane is __________ kg. (Take air density to be 1kg m-3 and g=10 ms-2) [2024]

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Q 5 : In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wings are 70 ms-1 and 65 ms-1 respectively. If the wing area is 2 m2 the lift of the wing is ______ N. (Given density of air = 1.2 kg m-1) [2024]

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Q 1 :
Correct Bernoulli's equation is (symbols have their usual meaning) [2024]

Q 5 :
In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wings are 70 ${ms}^{- 1}$ and 65 ${ms}^{- 1}$ respectively. If the wing area is 2 $m^{2}$ the lift of the wing is ______ N.

(Given density of air = 1.2 kg $m^{- 1}$ ) [2024]