Bernoulli's Principle

Q. A wind with speed $40\text{m/s}$ blows parallel to the roof of a house. The area of the roof is $250{\text{m}}^2$. Assuming that the pressure inside the house is equal to atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be $({\rho }_{\text{air}}=1.2{\text{kg/m}}^3)$

1. $2.4\times {10}^5\text{N, downwards}$
2. $4.8\times {10}^5\text{N, downwards}$
3. $4.8\times {10}^5\text{N, upwards}$
4. $2.4\times {10}^5\text{N, upwards}$

Q.

In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are $70m{s}^{–1}$ and $63m{s}^{–1}$ respectively. What is the lift on the wing if its area is 2.5 $m^2$? Take the density of air to be 1.3 kg $m^{–3}$.

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. Bernoulli's principle is based on the law of conservation of :

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

Q.

The cylindrical tube of a spray pump has a cross-section of $8.0c{m}^2$ one end of which has 40 fine holes each of diameter 1.0 mm. If the liquid flow inside the tube is $1.5mmi{n}^{–1}$, what is the speed of ejection of the liquid through the holes?

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. 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.

Venturimeter is a device used to measure the__________

Q.

Explain Bernoullis Principle.

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. Water flows through a horizontal pipe with a cross-sectional area of $2{\text{m}}^2$ at a speed of $5\text{m/s}$ with a pressure of $3\times {10}^5\text{Pa}$ at a point $A$. At point $B$, the cross-sectional area is $1{\text{m}}^2$. Calculate the pressure at point $B$.

1. $5\times {10}^5\text{Pa}$
2. $2.625\times {10}^5\text{Pa}$
3. $1.5\times {10}^5\text{Pa}$
4. $3\times {10}^4\text{Pa}$

Q. The kinetic energy of rotation of diatomic gas at ${27}^{\circ }$ will be $(k=1.38\times {10}^{-23}J/K)$

1. $3.07\times {10}^{-21}\text{Joule/molecule}$
2. $4.14\times {10}^{-21}\text{Joule/molecule}$
3. $2.07\times {10}^{-27}\text{Joule/molecule}$
4. $4.14\times {10}^{-21}\text{Joule/molecule}$

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

Q.

A plane is in level flight at constant speed and each of its two wings has an area of $25m^2$. 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 $1kg{m}^{–3})$.

Q. How does Bernoulli's theorem help in explaing blood flow in artery and cause of heart attack?

Q. In a horizontal pipeline of uniform cross-section the pressure falls by $8{\text{N/m}}^2$ between two points separated by $1\text{km}$. If oil of density $800{\text{kg/m}}^3$ flows through the pipe, find the change in $K.E$ per $\text{kg}$ of oil at these points.

1. ${10}^{-2}\text{J/kg}$
2. ${10}^{-3}\text{J/kg}$
3. ${10}^{-4}\text{J/kg}$
4. ${10}^{-1}\text{J/kg}$

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.

If the error in the measurement of the momentum of a particle is 100℅ then, what will be the error in measurement of kinetic energy of that particle?

Q. Calculate the mass flow rate of glycerin of density $1.25\times {10}^3{\text{kg/m}}^3$ through the conical section of a horizontal pipe, if the radii of its ends are $0.1\text{m}$ and $0.04\text{m}$ and pressure drop across its length is $10{\text{N/m}}^2$.

1. $0.96\text{kg/s}$
2. $0.785\text{kg/s}$
3. $0.6\text{kg/s}$
4. $0.34\text{kg/s}$

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.

Glycerine flows steadily through a horizontal tube of length 1.5 m and radius 1.0 cm. If the amount of glycerine collected per second at one end is $4.0\times {10}^{–3}kg{s}^{–1}$ , what is the pressure difference between the two ends of the tube? (Density of glycerine =$1.3\times {10}^{3}kg{m}^{–3}$ and viscosity of glycerine = 0.83 Pa s). [You may also like to check if the assumption of laminar flow in the tube is correct].

Q. A spherical body of mass $m$ and radius $r$ is allowed to fall in $\alpha$ medium of viscosity $\eta$. The time in which the velocity of the body increases from $0$ to $0.63$ times the terminal velocity $v$ called time constant $\tau$. Dimensionally $\tau$ can be represented by

1. $\frac{m}{6\pi \eta rv}$
2. $\sqrt{\left(\frac{6\pi mr\eta }{g^2}\right)}$
3. $\frac{m{r}^2}{6\pi \eta }$
4. None of the above

Q.

To which type of fluid is Bernoullis theorem applicable?

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 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. Water is flowing through a channel (lying in a vertical plane) as shown in the figure. Three sections $A,B$ and $C$ are shown. Section $B$ and $C$ have equal areas of cross- section. If $P_A,P_B$ and $P_C$ are the pressures at $A,B$ and $C$ respectively, then

1. $P_A<P_B=P_C$
2. $P_A<P_B<P_C$
3. $P_A>P_B>P_C$
4. $P_A>P_B=P_C$

Q. A liquid is kept in a cylindrical vessel which is rotated along its axis. The liquid rises at the sides as shown in figure below. If the radius of the vessel is 0.05 m and the speed of rotation is 2 rad $s^{-1}$, find the difference in the height of the liquid at the centre of the vessel and its sides

1. 0.2 cm
2. 4 cm
3. 20 cm
4. 2 cm

Q. The lift of an airplane is based on

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

Q.

Figures 10.23 (a) and (b) refer to the steady flow of a (non-viscous) liquid. Which of the two figures is incorrect? Why?

Q. A lead bullet penetrates into a solid object and melts. Assuming that $50\%$ of its kinetic energy was used to heat it, the initial speed (in $m/s$) of the bullet is
(the initial temperature of the bullet is ${27}^{\circ }C$ and its melting point is ${327}^{\circ }C$). Latent heat of fusion of lead $=2.5\times {10}^{4}J/kg$ and specific heat capacity of lead $=125J/kgK$