Equation of Continuity

Q.

The heart of a man pumps 5 litres of blood through the arteries per minute at a pressure of 150 $mm$ of mercury. If the density of mercury is $13.6\times {10}^{3}kg/m^3$ and $g=10m/s^2$ , then the power of heart in Watts is

1. $1.70$
2. $2.35$
3. $1.50$
4. $3.0$

Q. An incompressible liquid flows through a horizontal tube as shown in the figure. Then the velocity $v$ of the liquid coming out of the tube of area $1.5A$ is:

1. $1.0\text{m/s}$
2. $2.25\text{m/s}$
3. $3.0\text{m/s}$
4. $1.5\text{m/s}$

Q. The cylindrical tube of a spray pump has radius $R$. One end of the tube has $n$ fine holes each of radius $r$. If the speed of the liquid in the tube is $V$, then the speed of the ejection of the liquid through the holes is

1. $\frac{V^{2}R}{nr}$
2. $\frac{V{R}^2}{n^2{r}^2}$
3. $\frac{V{R}^2}{n{r}^2}$
4. $\frac{V{R}^2}{n^3{r}^2}$

Q. Water is flowing through a horizontal tube of non - uniform cross - section. At a place the radius of the tube is $1.0\text{cm}$ and the velocity of water is $2\text{m/s}$. Then, what will be the velocity of water at a point where the radius of the pipe is $2.0\text{cm}$?

1. $1\text{m/s}$
2. $0.25\text{m/s}$
3. $20\text{m/s}$
4. $0.5\text{m/s}$

Q. Water from a tap emerges vertically downwards with an initial speed of $1\text{m/s}$. The cross-section area of the tap is ${10}^{-4}{\text{m}}^2$ . Assuming that the pressure is constant throughout the stream of water and the flow is steady, what will be the cross-section area of the stream $0.15\text{m}$ below the tap?

1. $1.5\times {10}^{-5}{\text{m}}^2$
2. $4\times {10}^{-5}{\text{m}}^2$
3. $5\times {10}^{-5}{\text{m}}^2$
4. $2\times {10}^{-5}{\text{m}}^2$

Q.

Water flows in a horizontal tube. The pressure of water changes by 600 N m^-2between A and B where the areas of cross section are 30 cm² and 15 cm² respectively. Find the rate of flow of water through the tube. Given $\sqrt{0.4}$= 0.63 approx.

1. 1890 m³/s

2. 2260 cm³/s

3. 1890 cm³/s

4. 1664 cm³/s

Q.

At Deoprayag (Garhwal, UP) river Alaknanda mixes with the river Bhagirathi and becomes river Ganga. Suppose Alaknanda has a width of 12 m, Bhagirathi has a width of 8 m and Ganga has a width of 16 m. Assume that the depth of water is same in the three rivers. Let the average speed of water in Alaknanda be 20 km h^-1 and in Bhagirathi be 16 km h^-1. Find the average speed of water in the river Ganga.

1. 23 m/s

2. 23 km/hr

3. 46 km/hr

4. 46 m/s

Q. An ideal fluid is flowing in a pipe in a streamline flow. The pipe has a maximum and minimum diameter of $6.4\text{cm}$ and $4.8\text{cm}$ respectively. Find out the ratio of minimum to maximum velocity.

1. $\frac{3}{4}$
2. $\frac{3}{16}$
3. $\frac{81}{256}$
4. $\frac{9}{16}$

Q. Water is moving with a speed of $5.18m{s}^{-1}$ through a pipe with a cross-sectional area of $4.20c{m}^2$. The water gradually descends 9.66 m as the pipe increase in area to $7.60c{m}^2$. The speed of flow at the lower level is

1. 
2. 
3. 
4. 

Q. If a ball of steel (density ${\rho }_s=7.8{\text{g/cm}}^3$) attains a terminal velocity of $10\text{cm/s}$ when falling in a tank of water (coefficient of viscosity, ${\eta }_w=8.5\times {10}^{-4}\text{Pa-s}$). Then, its terminal velocity in glycerine (${\rho }_g=1.2{\text{g/cm}}^3,{\eta }_g=13.2\text{Pa-s}$) would be nearly:

1. $1.6\times {10}^{-5}\text{cm/s}$
2. $1.5\times {10}^{-5}\text{cm/s}$
3. $6.45\times {10}^{-4}\text{cm/s}$
4. $6.25\times {10}^{-4}\text{cm/s}$

Q. An incompressible liquid is flowing through the horizontal pipe as shown in the figure. Pipe $1$ is connected to the pipe $2$ and pipe $3$. The flow of liquid through the pipe $1$, pipe $2$ and pipe $3$ are $8\text{m/s},6\text{m/s}$ and $1.1\text{m/s}$ respectively. If cross-section area of pipe $1$ and pipe $2$ are $1{\text{m}}^2$ and $0.8{\text{m}}^2$, find the area of cross-section of pipe $3$.

1. $4.6{\text{m}}^2$
2. $16.5{\text{m}}^2$
3. $2.9{\text{m}}^2$
4. $5.8{\text{m}}^2$

Q.

Is escape velocity greater than orbital velocity?

Q.

Water enters through end A with a speed v₁ and leaves through end B with a speed v₂ of a cylindrical tube AB. The tube is always completely filled with water. In case I the tube is horizontal, in case II it is vertical with the end A upward and in case III it is vertical with the end B upward. We have v₁ = v₂ for

1. Case I

2. Case II

3. Case III

4. each case

Q. Water is flowing through two horizontal pipes of different diameters which are connected together. The diameter of the two pipes are $3\text{cm}$ and $6\text{cm}$ respectively. If the speed of water in the narrower tube is $4\text{m/s}$, then the speed of water in the wider tube is

1. $16\text{m/s}$
2. $1\text{m/s}$
3. $4\text{m/s}$
4. $2\text{m/s}$

Q.

Why are conservation of mass and conservation of mechanical energy not considered fundamental laws of nature?

Q. A liquid flows in the tube from left to right as shown in figure. $A_1$ and $A_2$ are the area of cross - sections of the portions of the tube as shown. If speed of liquid in these portions be $V_1\&V_2$ respectively . The ratio of speeds $\frac{V_1}{V_2}$ will be

1. $\sqrt{\frac{A_2}{A_1}}$
2. $\sqrt{\frac{A_1}{A_2}}$
3. $\frac{A_1}{A_2}$
4. $\frac{A_2}{A_1}$

Q. A syringe of diameter $1\text{cm}$ having a nozzle of diameter $1\text{mm}$, is placed horizontally at a height $5\text{m}$ from the ground. An incompressible, non-viscous liquid is filled in the syringe and the liquid is compressed by moving the piston at a speed of $0.5{\text{ms}}^{-1}$. The horizontal distance travelled by the liquid jet is $(g=10{\text{ms}}^{-2})$

1. $12.5\text{m}$
2. $25\text{m}$
3. $50\text{m}$
4. $67.5\text{m}$

Q.

An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are $6.4cm$ and $4.8cm$, respectively. The ratio of minimum and maximum velocities of fluid in this pipe is

1. $\raisebox{1ex}{$\sqrt{3}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

2. $\raisebox{1ex}{$9$}\!\left/ \!\raisebox{-1ex}{$16$}\right.$

3. $\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$

4. $\raisebox{1ex}{$\sqrt{3}$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$

Q. Water flows through a non - uniform tube of area of cross - section $\text{A, B}$ and $\text{C}$ whose values are $25,15$ and $35{\text{cm}}^2$ respectively. The ratio of the velocity of water at the sections $\text{A, B}$ and $\text{C}$ is

1. 5 : 3 : 7
2. 7 : 3 : 5
3. 1 : 1 : 1
4. 21 : 35 : 15

Q. A liquid flows in the tube, left to right as shown in figure. $d_1$ and $d_2$ are the diameter of tube as shown in figure. Find the ratio of speed $\frac{V_1}{V_2}$.

1. $\frac{1}{8}$
2. $\frac{1}{4}$
3. $\frac{1}{2}$
4. $\frac{1}{16}$

Q. Fresh water issues from the nozzle with a velocity of $20m/sec$ at the rate of $0.03m^3/sec$ and is split into two equal streams by the fixed vane and deflected through ${60}^{\circ }$ as shown in figure. The force in newtons required to hold the vane in place is
(Assume area of cross section of water in each stream in $A$)

Q. The intake in figure has cross-sectional area of $0.74{\text{m}}^2$ and water flow at $0.40\text{m/s}$. At the outlet, distance $D=180\text{m}$ below the intake, the cross sectional area is smaller than at the intake and the water flows out at $9.5\text{m/s}$ into equipment. What is the pressure difference between inlet and outlet?

1. $3.14\text{MPa}$
2. $2\text{MPa}$
3. $1.71\text{MPa}$
4. $6.2\text{MPa}$

Q. A liquid is under streamline flow through a horizontal pipe of non uniform cross-sectional area. If the volume rate of flow at a cross-section of area $a$ is $V$, then volume rate of flow at a different cross-section of area $\frac{a}{2}$ is

1. $V$
2. $2V$
3. $\frac{V}{2}$
4. $\frac{V}{4}$

Q. A liquid flows in the tube from left to right as shown in figure. $A_1$ and $A_2$ are the area of cross - sections of the portions of the tube as shown. If speed of liquid in these portions be $V_1\&V_2$ respectively . The ratio of speeds $\frac{V_1}{V_2}$ will be

1. $\frac{A_1}{A_2}$
2. $\frac{A_2}{A_1}$
3. $\sqrt{\frac{A_2}{A_1}}$
4. $\sqrt{\frac{A_1}{A_2}}$

Q. A liquid with speed $v$ through a horizontal pipe of cross sectional area $A$ enters into another pipe of double the area of cross-section. The speed of the liquid in the second pipe will be

1. $v$
2. $\frac{v}{2}$
3. $2v$
4. $\frac{v}{4}$

Q. "The velocity of entrance and exit through a nozzle remains the same ", is this ever possible?

1. Only if the flow is compressible
2. Only if the flow is laminar
3. Only if the flow is rotational
4. Never possible

Q. The equation of continuity is obtained as a result of which of the following laws?

1. Law of conservation of momentum for liquid flow
2. Law of conservation of energy
3. Law of equipartition of energy
4. Law of conservation of mass

Q. The rate of flow of the liquid is the product of

1. Area of cross section of the liquid and velocity of the liquid.
2. Viscous force acting on the liquid layer and velocity of the liquid
3. Length of the tube of the flow and velocity of the liquid
4. Volume of the tube of the flow and velocity of the liquid

Q. The pipe shows the volume flow rate of an ideal liquid at a certain time and its direction. What is the value of $Q$ in $\text{m}{}^3\text{/s}$?(Assume steady state and equal area of cross section at each opening)

1. $10\times {10}^{-6}$
2. $18\times {10}^{-6}$
3. $13\times {10}^{-6}$
4. $11\times {10}^{-6}$

Q. The cylindrical tube of a spray pump has radius of $5\text{cm}$, one end of which has $10$ fine holes each of radius $0.1\text{cm}$. If the speed of liquid in the tube is $1\text{m/s}$, the speed of the ejection of the liquid through the holes is

1. $125\text{m/s}$
2. $250\text{m/s}$
3. $450\text{m/s}$
4. $500\text{m/s}$