Q. No.A cylindrical vessel of \(40~\text{cm}\) radius is completely filled with water and its capacity is \(528~\text{dm}^3\) (dm : decimeter) The vessel is placed on a solid block of exactly same height as vessel. If a small hole is made at \(70~\text{cm}\) below the top of water level, then horizontal range of water falling on the ground in the beginning is: (in cm)
1. \(120 \sqrt{2} \)
2. \(140 \sqrt{2} \)
3. \(140 \sqrt{3} \)
4. \(120 \sqrt{3}\)
1. \(120 \sqrt{2} \)
2. \(140 \sqrt{2} \)
3. \(140 \sqrt{3} \)
4. \(120 \sqrt{3}\)
Subtopic: Bernoulli's Theorem |
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Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is \(5~\text{cm}\) and the area of cross-sections at \(A\) and \(B\) are \(6~\text{cm}^2\) and \(3~\text{cm}^2\) respectively.
The rate of flow will be: (in \(\text{cm}^3/\text{s}\)). (take \(g = 10~\text{m/s}^2\))
1. \(\dfrac{200}{\sqrt{3}}\)
2. \(200 \sqrt{6}\)
3. \(200 \sqrt{3}\)
4. \(100 \sqrt{3}\)
The rate of flow will be: (in \(\text{cm}^3/\text{s}\)). (take \(g = 10~\text{m/s}^2\))
1. \(\dfrac{200}{\sqrt{3}}\)
2. \(200 \sqrt{6}\)
3. \(200 \sqrt{3}\)
4. \(100 \sqrt{3}\)
Subtopic: Bernoulli's Theorem |
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Consider a completely full cylindrical water tank of height \(1.6 ~\text m\) and of cross-sectional area \(0.5 ~\text m^2 .\) It has a small hole in its side at a height \(90 \text{ cm} \) from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load \(50 ~\text{kg}\) is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is: \((g=10 \text{ m/s}^2 ) \)
1. \(3\text{ m/s} ~\)
2. \(2\text{ m/s} ~\)
3. \(4\text{ m/s} ~\)
4. \(5\text{ m/s} ~\)
1. \(3\text{ m/s} ~\)
2. \(2\text{ m/s} ~\)
3. \(4\text{ m/s} ~\)
4. \(5\text{ m/s} ~\)
Subtopic: Bernoulli's Theorem |
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Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is \(P_1.\) The reading of the pressure gauge falls to \(P_2\) when the valve is opened. The speed of water flowing in the pipe is proportional to
1. \(\left(P_1-P_2\right)^2 \)
2. \(P_1-P_2\)
3. \(\left(P_1-P_2\right)^4 \)
4. \(\sqrt{\left(P_1-P_2\right)}\)
1. \(\left(P_1-P_2\right)^2 \)
2. \(P_1-P_2\)
3. \(\left(P_1-P_2\right)^4 \)
4. \(\sqrt{\left(P_1-P_2\right)}\)
Subtopic: Bernoulli's Theorem |
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The correct Bernoulli's equation is (symbols have their usual meaning):
1. \(P+\rho g h+\dfrac{1}{2} \rho v^2=\text { constant }\)
2. \({P}+\rho {gh}+\rho {v}^2=\text{constant}\)
3. \(P+{mgh}+\dfrac{1}{2} {mv}^2=\text { constant }\)
4. \({P}+\dfrac{1}{2} \rho g h+\dfrac{1}{2} \rho {v}^2=\text { constant }\)
1. \(P+\rho g h+\dfrac{1}{2} \rho v^2=\text { constant }\)
2. \({P}+\rho {gh}+\rho {v}^2=\text{constant}\)
3. \(P+{mgh}+\dfrac{1}{2} {mv}^2=\text { constant }\)
4. \({P}+\dfrac{1}{2} \rho g h+\dfrac{1}{2} \rho {v}^2=\text { constant }\)
Subtopic: Bernoulli's Theorem |
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The pressures at the ends of a horizontal pipe are given for water. The speed \({v}\) at end \(2\) if the speed at end \(1\) is \(10~\text{m/s}.\) (density of water \(=1000~\text{kg/m}^3\)). Then the speed \({v}\) (in \(\text{m/s}\)) is:
1. \(22\)
2. \(33\)
3. \(11\)
4. \(55\)
1. \(22\)
2. \(33\)
3. \(11\)
4. \(55\)
Subtopic: Bernoulli's Theorem |
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In a pipe carrying an ideal liquid, the flow speed is \(v_1\) at point \(A\) and \(v_2\) at point \(B.\) The diagram shows a pipe with two vertical tubes (manometers) connected to it. The liquid rises to different heights in these tubes, with a height difference of \(h\) between them.
(where \(g\) is the acceleration due to gravity and \(\rho\) is the density of the liquid)
What is the correct relationship between \(v_1,\) \(v_2\) and \(h\text{?}\)
(where \(g\) is the acceleration due to gravity and \(\rho\) is the density of the liquid)
What is the correct relationship between \(v_1,\) \(v_2\) and \(h\text{?}\)
| 1. | \(v_2^2=v_1^2+2 g h \) | 2. | \(v_1 v_2=2 g h \) |
| 3. | \(v_1^2 v_2=\rho g h^2 \) | 4. | \(v_2^2-v_1^2+2 g h=0\) |
Subtopic: Bernoulli's Theorem |
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Water is flowing inside the conical type tube having a ratio of area of cross-section \(6:1\). If the speed of the water outlet through a smaller area is \(60~\text{m/s}\), then the pressure difference across these two cross-sections is:
(assume incompressible fluid, density of water = \(1000~\text{kg/m}^3\) )
1. \(175\times 10^4~ \text{Pa}\)
2. \(175\times 10^3~ \text{Pa}\)
3. \(250\times 10^4~ \text{Pa}\)
4. \(250\times 10^3~ \text{Pa}\)
(assume incompressible fluid, density of water = \(1000~\text{kg/m}^3\) )
1. \(175\times 10^4~ \text{Pa}\)
2. \(175\times 10^3~ \text{Pa}\)
3. \(250\times 10^4~ \text{Pa}\)
4. \(250\times 10^3~ \text{Pa}\)
Subtopic: Bernoulli's Theorem |
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A liquid of density \(750~\text{kgm}^{-3}\) flows smoothly through a horizontal pipe that tapers in cross-sectional area from \(A_1 = 1.2 \times 10^{-2}~\text{m}^2\) to \(A_2 = \dfrac{A_1}{2}.\) The pressure difference between the wide and narrow sections of the pipe is \(4500~\text{Pa}.\) The rate of flow of liquid is:
1. \(20\times 10^{-3}~\text{m}^{-3}\text{s}^{-1}\)
2. \(30\times 10^{-3}~\text{m}^{-3}\text{s}^{-1}\)
3. \(28\times 10^{-3}~\text{m}^{-3}\text{s}^{-1}\)
4. \(24\times 10^{-3}~\text{m}^{-3}\text{s}^{-1}\)
1. \(20\times 10^{-3}~\text{m}^{-3}\text{s}^{-1}\)
2. \(30\times 10^{-3}~\text{m}^{-3}\text{s}^{-1}\)
3. \(28\times 10^{-3}~\text{m}^{-3}\text{s}^{-1}\)
4. \(24\times 10^{-3}~\text{m}^{-3}\text{s}^{-1}\)
Subtopic: Bernoulli's Theorem |
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The area of the cross-section of a large tank is \(0.5~\text{m}^2\). It has a narrow opening near the bottom having an area of cross-section \(1~\text{cm}^2\). A load of \(25~\text{kg}\) is applied on the water at the top of the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of the water level in the tank is \(40~\text{cm}\) above the bottom, will be: [Take \(g = 10~\text{ms}^{-2}\)]
1. \(1~\text{ms}^{-1}\)
2. \(2~\text{ms}^{-1}\)
3. \(3~\text{ms}^{-1}\)
4. \(4~\text{ms}^{-1}\)
1. \(1~\text{ms}^{-1}\)
2. \(2~\text{ms}^{-1}\)
3. \(3~\text{ms}^{-1}\)
4. \(4~\text{ms}^{-1}\)
Subtopic: Bernoulli's Theorem |
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