Bernoulli's Principle

Q.

Consider a water tank as shown in the figure. It’s cross-sectional area is $0.4m^2$. The tank has an opening $B$ near the bottom whose cross-sectional area is $1c{m}^2$. A load of $24kg$ is applied on the water at the top when the height of the water level is $40cm$ above the bottom, the velocity of water coming out the opening $B$ is $vm{s}^{-1}$. The value of $v$, to the nearest integer, is $\_\_\_\_.$

[Take value of $g$ to be $10m{s}^{-2}$]

Q. A liquid is kept in a cylindrical vessel which is being rotated about a vertical axis through the centre of the circular base. If the radius of the vessel is r and angular velocity of rotation is $\omega$, then the difference in the heights of the liquid at the centre of the vessel and the edge is

1. 
2. 
3. 
4. 

Q.

A thermally isolated cylindrical closed vessel of height $8m$ is kept vertically. It is divided into two equal parts by a diathermic (perfect thermal conductor) frictionless partition of mass $8.3kg$. Thus, the partition is held initially at a distance of $4m$ from the top, as shown in the schematic figure below. Each of the two parts of the vessel contains $0.1mole$ of an ideal gas at temperature $300K$. The partition is now released and moves without any gas leaking from one part of the vessel to the other. When equilibrium is reached, the distance of the partition from the top (in $m$) will be _______

(Take the acceleration due to gravity = $10m{s}^{-2}$ and the universal gas constant =$8.3Jmo{l}^{-1}{K}^{-1}$).

Q.

A manometer connected to a closed tap reads 3.5 $\times$ ${10}^5$ N/$m^2$. When the valve is opened, the reading of manometer falls to 3.0 $\times$ ${10}^5$ N/$m^2$, then velocity of flow of water is

1. 100 m/s

2. 10 m/s

3. 10 .10m/s

4. 1 m/s

Q. Two capillaries of same length and radii in the ratio 1 is to 2 are connected in series. A liquid flows through them in streamlined condition. If the pressure across the two ends of the combi ation is 1m of water, the pressure difference across first capillary is

Q. Explain why (a) To keep a piece of paper horizontal, you should blow over, not under, it (b) When we try to close a water tap with our fingers, fast jets of water gush through the openings between our fingers (c) The size of the needle of a syringe controls flow rate better than the thumb pressure exerted by a doctor while administering an injection (d) A fluid flowing out of a small hole in a vessel results in a backward thrust on the vessel (e) A spinning cricket ball in air does not follow a parabolic trajectory

Q.

A liquid is coming out from a vertical tube. The relation between the weight of the drop W, surface tension of the liquid T and radius of the tube r is given by, if the angle of contact is zero

1. 

2. 

3. T

4. 

Q.

An ideal liquid is streamline motion flows through a frictionless duct with varying cross-section as shown in figure.

Pressure P at points along the x axis of duct is most likely to be represented by :

1. 

2. 

3. 

4. 

Q.

An ideal liquid of density $\rho$ is pushed with velocity v through the central limb of the tube shown in fig. What force does the liquid exert on the tube? The cross sectional areas of the three limbs are equal to A each. Assume stream-line flow.

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2. 

3. 

4. 

Q. how to calculate pressure in liquids

Q.

A liquid flows through a horizontal tube. The velocities of the liquid in the two sections, which have have areas of cross section $A_1$ and $A_2$, are $v_1$ and $v_2$ respectively. The difference in the levels of the liquid in the two vertical tubes is $h$. Then :

1. The volume of the liquid flowing through the tube in unit time is $A_1{v}_1$.
2. $v_2-v_1=\sqrt{2gh}$
3. $v_2^2-v_1^2=2gh$
4. The energy per unit volume of the liquid is the same in both sections of the tube.

Q.

Water and mercury are filled in two cylindrical vessels upto same height. Both vessels have a hole in the wall near the bottom. The velocity of water and mercury coming out of the holes are $v_1$ and $v_2$ respectively. Thus

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2. 

3. 

4. 

Q. Assertion :A particle in x-y plane is related by x=a sin(wt) and y=a (1-cos wt), where a and w are constants then the particle has parabolic motion. Reason:A particle under the influence of two perpendicular velocities has parabolic velocity.

Q. 33. Liquid filled in the container has density 5 kg/m3. If the container is moving horizontally with acceleration as2 m/s2 then pressure difference between two points A and B, which are at the same level with separationbetween them 50 cm, will be50 cm2(2) 2.5 N/m2(4) Zero(3) 7.5 N/m2alinuid fillad in a cantainer will make with horizontal if the containe

Q. atank is filled with water to a height H. A hole is made in one of the walls at a depth D below the water surface. The distance x from the foot of the wall at which the stream of water coming out of the tank strikes the ground is given by (1)x -2 \lbrack D (H- D)\rbrack^{1/2} (2) x= 2 (gD)^{1/2 }(3) x= 2 D (H+ D)^{1/2}4) None of these

Q.

Water is flowing through a horizontal tube. The pressure of the liquid in the portion where velocity is 2 m/s is 2 m of Hg. What will be the pressure in the portion where velocity is 4 m/s?

1. 4.3 x 10³ Pa

2. 0.43 x 10³ Pa

3. 43 x 10³ Pa

4. 430 x 10³ Pa

Q. A ball is dropped from a height of 90 m on a floor. At each collision with the floor, the ball loses one tenth of its speed. Plot the speed-time graph of its motion between t = 0 to 12 s.

Q. Water from a tap emerges vertically downwards with initial velocity $4{\text{ms}}^{-1}$. The cross-sectional area of the tap is $A$. The flow is steady and pressure is constant throughout the stream of water. The distance $h$ vertically below the tap, where the cross-sectional area of the stream becomes $\frac{2}{3}A$, is:
[Take $g=10{\text{m/s}}^2$]

1. $0.5\text{m}$
2. $1\text{m}$
3. $1.5\text{m}$
4. $2.2\text{m}$

Q.

A venturimeter is used to

1. measure flow speed of incompressible fluid

2. measure speed of a freely falling body in the fluid

3. measure atmospheric pressure

4. find viscosity of a fluid

Q.

What is the Significance of Bernoullis Principle?

Q. Water flows steadily through a horizontal tube of variable cross-section. If the pressure of water is $P$ at a point where the velocity of flow is $v$, what is the pressure at another point where the velocity of flow is $2v$; $\rho$ being the density of water?

1. $P-\frac{3}{2}\rho v^2$
2. $P+\frac{3}{2}\rho v^2$
3. $P-2p{v}^2$
4. $P+\frac{1}{2}\rho v^2$

Q. In old age arteries carrying blood in the human body become narrow resulting in an increase in the blood pressure. This follows from :

1. Pascal's law
2. Stoke's law
3. Bernoulli's principle
4. Archimedes principle

Q. A non-viscous liquid of constant density $1000{\text{kg/m}}^3$ flows in a streamline motion along a tube of variable cross-section. The tube is kept inclined in a vertical plane, as shown in the figure and the velocity of the liquid at point $A$ is $1\text{m/s}$. The area of cross-section of the tube at two points $A$ and $B$ at heights $2\text{m}$ and $5\text{m}$ are $4\times {10}^{-3}{\text{m}}^2$ and $8\times {10}^{-3}{\text{m}}^2$ respectively. Then:

1. outlet velocity of liquid at point B is $0.5\text{m/s}$.
2. work done by pressure per unit volume is $4.956\times {10}^4{\text{J/m}}^3$
3. work done by gravity per unit volume is $-3\times {10}^4{\text{J/m}}^3$
4. work done by gravity per unit volume is $-6\times {10}^4{\text{J/m}}^3$

Q. In the below given problem, if 15.0 cm of water and spirit each are further poured into the respective arms of the tube, what is the difference in the levels of mercury in the two arms ? (Specific gravity of mercury = 13.6)
Problem:[A U-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with 10.0 cm of water in one arm and 12.5 cm of spirit in the other ]

Q. A plane is in level flight at constant speed and each of its two wings has an area of 25 m². If the speed of the air is 180 km/h over the lower wing and 234 km/h over the upper wing surface, determine the plane’s mass. (Take air density to be 1 kg m¯³).

Q. The flow speeds of air on the lower and upper surfaces of the wing of an aeroplane are $v$ and $\sqrt{2}v$ respectively. The density of air is $\rho$ and surface area of wing is $A$. The dynamic lift on the wing is:

1. $\rho v^{2}A$
2. $\sqrt{2}\rho v^{2}A$
3. $\left(\frac{1}{2}\right)\rho v^{2}A$
4. $2\rho v^{2}A$

Q. A plane is in a level flight at a constant speed and each of its two wings has an area of $50{\text{m}}^2$. If the speed of air is $180\text{km/h}$ over the lower wing surface and $252\text{km/h}$ over the upper wing surface, the plane's mass is [Lift force on the wings = weight of plane]
(Take density of air = $1{\text{kg/m}}^3$ and $g=10{\text{m/s}}^2$)

1. $2.4\times {10}^4\text{kg}$
2. $4.4\times {10}^4\text{kg}$
3. $1.2\times {10}^4\text{kg}$
4. $3.6\times {10}^4\text{kg}$

Q.

The equation of continuity is a special case of the law of conservation of

1. Momentum

2. Angular momentum

3. Energy

4. Mass

Q. A fire hydrant delivers water of density at a volume rate L. The water travels vertically upwards through the hydrant and then does 90 turn to emerge horizontally at speed v. The pipe and nozzle have uniform cross section throughout. The force exerted by water on the corner of the hydrant is

1. zero
2. $\rho vL$
3. $\sqrt{2}\rho vL$
4. $2\rho vL$

Q. Can Bernoulli's equation be used to describe the flow of water through a rapid in a river ? Explain.