Bernoulli's Principle

Q. The lift of an airplane is based on

1. Torricelli's theorem
2. Bernoulli's theorem
3. Law of gravitation
4. Conservation of linear momentum

Q. An ideal fluid is flowing through the given tubes which is placed on a horizontal surface. If the liquid has velocities $v_A$ and $v_B$, and pressures $P_A$ and $P_B$ at points $A$ and $B$ respectively, then the correct relation is:
(The figure shown below is as if the system is seen from the top)

1. $v_A>v_B,P_A<P_B$
2. $v_A<v_B,P_A>P_B$
3. $v_A=v_B,P_A=P_B$
4. $v_A>v_B,P_A=P_B$

Q.

An ideal liquid (water) flowing through a tube of non-uniform cross-sectional area, where area at $A$ and $B$ are $40c{m}^2$ and $20c{m}^2$ respectively. If pressure difference between $A$ and $B$ is $700\raisebox{1ex}{$N$}\!\left/ \!\raisebox{-1ex}{$m^2$}\right.$, then volume flow rate is (density of water = $1000\raisebox{1ex}{$kg$}\!\left/ \!\raisebox{-1ex}{$m^3$}\right.$)

1. $2720\raisebox{1ex}{$c{m}^3$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

2. $2420\raisebox{1ex}{$c{m}^3$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

3. $1810\raisebox{1ex}{$c{m}^3$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

4. $3020\raisebox{1ex}{$c{m}^3$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Q. Bernoulli's theorem is a consequence of

1. conservation of mass
2. conservation of energy
3. conservation of linear momentum
4. conservation of angular momentum

Q. Choose the correct option
Assertion: Bernoulli's equation hold for non-steady and compressible flow.
Reason: For non-steady flow, velocity and pressure are constant with time.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Q. In the following figure, flow of a liquid through a horizontal pipe has been shown. Three tubes $A,B$ and $C$ are connected to the pipe. The radii of the tubes $A,B$ and $C$ at the junction are respectively $2\text{cm},1\text{cm}$ and $2\text{cm}$. It can be said that the

1. height of the liquid in the tube $B$ is maximum
2. height of the liquid in the tubes $A$ and $B$ is the same
3. height of the liquid in all the three tubes is the same
4. height of the liquid in the tubes $A$ and $C$ is the same.

Q. Figure shows a stream of water emerging from the opening of a tap. As the water falls through a height $h=PQ$, the cross-sectional area of the stream decreases from $A$ to $a$. Obtain the expression for the rate of flow of water through the opening of the tap.

1. $a^2{\left[\frac{2gh}{A^2-a^2}\right]}^{1/2}$
2. $A^2{\left[\frac{2gh}{A^2-a^2}\right]}^{1/2}$
3. $aA{\left[\frac{2gh}{A^2-a^2}\right]}^{1/2}$
4. $A^2{\left[\frac{gh}{A^2-a^2}\right]}^{1/2}$

Q. Kerosene oil is flowing through a pipe having constant cross section area with diameter $2.5\text{cm}$, at a rate of $10\text{litre/sec}$. The height of bottom and top end is $2\text{m}$ and $8\text{m}$ respectively from the datum line. Find the pressure at the lower end, if the pressure at the other end is $25\times {10}^4{\text{N/m}}^2$. (Density of kerosene $=850{\text{kg/m}}^3)$

1. $2.51\times {10}^4{\text{N/m}}^2$
2. $1.51\times {10}^5{\text{N/m}}^2$
3. $2\times {10}^5{\text{N/m}}^2$
4. $3.01\times {10}^5{\text{N/m}}^2$

Q. The lift of an airplane is based on

1. Torricelli's theorem
2. Bernoulli's theorem
3. Law of gravitation
4. Conservation of linear momentum

Q. Water flows along a horizontal pipe of non-uniform cross-section. The pressure is $1\text{cm}$ of $Hg$ where the velocity is $35\text{cm/s}$. At a point where the velocity is $65\text{cm/s}$, the pressure will be

1. $0.89\text{cm}$ of $Hg$
2. $0.62\text{cm}$ of $Hg$
3. $0.5\text{cm}$ of $Hg$
4. $1\text{cm}$ of $Hg$

Q. A horizontal pipeline carries water in a streamline flow. At a point where the cross-sectional area is $10{\text{cm}}^2$, the water velocity is $1{\text{ms}}^{-1}$ and pressure is $2000\text{Pa}$. The pressure of water at another point where the cross sectional area is $5{\text{cm}}^2$, is:

1. $200\text{Pa}$
2. $400\text{Pa}$
3. $500\text{Pa}$
4. $800\text{Pa}$

Q. Water flows through a vertical tube of variable cross section. The area of cross - section at $A$ and $B$ are $6{\text{mm}}^2$ and $3{\text{mm}}^2$ respectively. If $12{\text{cm}}^3$ of water enters per second through $A$, find the pressure difference $|P_A-P_B|$. The separation between the cross-section at $A$ and $B$ is $100\text{cm}$. (Take density of water as $1000{\text{kg/m}}^3$ and $g=10{\text{m/s}}^2$)

1. $7000{\text{N/m}}^2$
2. $3000{\text{N/m}}^2$
3. $6000{\text{N/m}}^2$
4. $4000{\text{N/m}}^2$

Q. In the case of motion of a fluid in a tube where area of cross-section is maximum,
a) velocity is maximum
b) pressure is maximum
c) velocity is minimum
d) pressure is minimum

1. b, c are correct
2. a, d are correct
3. a, b are correct
4. c, d are correct

Q. Water enters a pipe with inlet diameter of $1.5\text{cm}$ at an absolute pressure of $5\times {10}^5\text{Pa}$. The outlet of the pipe is $1\text{cm}$ in diameter and is at height of $6\text{m}$ above the inlet. When the flow speed at the inlet pipe is $2\text{m/s}$. Find the flow speed $\left(\text{m/s}\right)$ and pressure $\left(\text{Bar}\right)$ at the outlet of the pipe. (Take $g=10{\text{m/s}}^2$)

1. $4.5\text{m/s},4.3\times {10}^5\text{Pa}$
2. $9\text{m/s},4.3\times {10}^5\text{Pa}$
3. $4.5\text{m/s},8.6\times {10}^5\text{Pa}$
4. $9\text{m/s},4.3\times {10}^5\text{Pa}$

Q. Choose the correct option
Assertion: Bernoulli's equation hold for non-steady and compressible flow.
Reason: For non-steady flow, velocity and pressure are constant with time.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

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

1. $100\text{m/s}$
2. $10\text{m/s}$
3. $1\text{m/s}$
4. $10\sqrt{10}\text{m/s}$

Q. An ideal fluid is flowing through the given tubes which are placed on a horizontal surface. If the liquid has velocities $V_A$ and $V_B$, and pressure $P_A$ and $P_B$ at points A and B respectively, then the correct relation is (A and B are at the same height from ground level, the figure shown is as if the system is seen from the top):

1. $V_A=V_B,P_A=P_B$
2. $V_A>V_B,P_A<P_B$
3. $V_A>V_B,P_A=P_B$
4. $V_A<V_B,P_A>P_B$

Q. In a horizontal pipeline of variable cross-section, $2\times {10}^{-2}\text{J/kg}$ is the change in kinetic energy per $\text{kg}$ of the kerosene oil flowing through the pipe of length $1500\text{m}$. What will be the pressure drop between the end points of the pipe? (Take density of kerosene oil as $850{\text{kg/m}}^3)$

1. $8{\text{N/m}}^2$
2. $10{\text{N/m}}^2$
3. $17{\text{N/m}}^2$
4. $1.34{\text{N/m}}^2$

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. Aerofoils are so designed that the speed of air

1. on top side is more than that on lower side
2. on top side is less than that on lower side
3. is same on both sides
4. None of the above

Q. Water is flowing continuously from a tap having an internal diameter $8\times {10}^{-3}\text{m}$. The water velocity as it leaves the tap is $0.4\text{m/s}$. The diameter of the water stream at a distance $2\times {10}^{-1}\text{m}$ below the tap is close to

1. $\frac{8}{\sqrt[4]{426}}\text{mm}.$
2. $\frac{8}{\sqrt[4]{436}}\text{mm}$
3. $\frac{6}{\sqrt[2]{228}}\text{mm}$
4. $\frac{4}{\sqrt[3]{334}}\text{mm}$

Q. Water flows through a frictionless duct with a cross-section varying as shown in the figure. The pressure $P$ at points along the axis (starting from left end to right end) is represented by

1. 
2. 
3. 
4. 

Q. Air streams horizontally past an airplane. The speed of air over the top surface of the wings is $60\text{m/s}$ and that under the bottom surface is $45\text{m/s}$. The density of air is $1.293{\text{kg/m}}^3$. Then, the difference in pressure between the top and bottom surface of the wings is:
(Consider airplane to be flying at a constant altitude)

1. $1018{\text{N/m}}^2$
2. $516{\text{N/m}}^2$
3. $1140{\text{N/m}}^2$
4. $2250{\text{N/m}}^2$

Q.

Air is streaming past a horizontal air plane wing such that its speed is 120m/s over the upper surface and 90 m/s at the lower surface. If the density of air is 1.3 kg per $metr{e}^3$ and the wing is 10 m long and has an average width of 2 m, then the difference of the pressure on the two sides of the wing is

1. 4095.0 Pascal

2. 409.50 Pascal

3. 40.950 Pascal

4. 4.0950 Pascal

Q. A non-viscous liquid is flowing through a non-uniform pipe from section $A$ to section $B$ as shown in the following figure. Cross-sectional area of the pipe at $A$ is less than that at $B$. Which of the following statements are correct?

1. The pressure at $A$ is greater than that at $B$
2. Velocity at $A$ is greater than that at $B$
3. Total energy per unit volume of the liquid is greater at $A$ than at $B$
4. Axis of the pipe cannot be horizontal

Q. Water flows steadily through a horizontal pipe of a 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. $p-2\rho v^2$
4. $p+2\rho v^2$

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. As shown in the figure a liquid of density $\rho$ is kept in a sealed container. The height of liquid column is $h$. The container contains compressed air at a gauge pressure of $p$. The horizontal pipe has a outlet with cross-sectional area $A/2$ at $E$, where $A$ is the cross-sectional area of the horizontal pipe. Choose the correct option(s).

1. The velocity of liquid at $C$ will be ${\left[\frac{(p+\rho gh)}{2\rho }\right]}^{1/2}$
2. The velocity of liquid at $C$ will be ${\left[\frac{2(p+\rho gh)}{\rho }\right]}^{1/2}$
3. The discharge rate is given by $\frac{A}{2\rho }(p+\rho gh{)}^{1/2}$
4. The discharge rate is given by $\frac{A}{\sqrt{2\rho }}(p+\rho gh{)}^{1/2}$

Q. A non-viscous liquid flows through a horizontal pipe of varying cross-sectional area. Identify the option which correctly represents the variation of height of rise of liquid in each vertical tube.

1. 
2. 
3. 
4. 

Q. Air streams flows horizontally past an air plane. The speed over the top surface is $50\text{m/s}$ and that under the bottom surface is $40\text{m/s}$. If the density of air is $1.2{\text{kg/m}}^3$, then the difference in pressure across the plane is

1. $1160{\text{N/m}}^2$
2. $540{\text{N/m}}^2$
3. $280{\text{N/m}}^2$
4. $12.84{\text{N/m}}^2$