Equation of Continuity

Q.

The human heart forces 4500 cc of blood per min through the arteries, under a pressure of 15 cm of Hg. Calculate the hp of the heart.
Take 1 hp = 746 W and g = 980 cm/s².

Q.

If the heart pushes $1\mathrm{cc}$ of blood in $1\mathrm{s}$ under pressure $20000{\mathrm{Nm}}^{-2},$ the power of the heart is

1. $0.02\mathrm{W}$

2. $400\mathrm{W}$

3. $5\times {10}^{-10}\mathrm{W}$

4. $0.2\mathrm{W}$

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

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. 21 : 35 : 15
4. 1 : 1 : 1

Q. Water is flowing through a horizontal tube of non-uniform cross section. At a place, the radius of the tube is $2\text{cm}$ and velocity is $6\text{m/s}$. What will be the velocity of water where the radius of pipe is $4\text{cm}$?

1. $6\text{m/s}$
2. $1.5\text{m/s}$
3. $3\text{m/s}$
4. $2\text{m/s}$

Q.

In the figure shown, a liquid is flowing through a tube at the rate of 0.1 $m^3$/sec. The tube is randed into two semicircular tubes of cross sectional area $\frac{A}{3}$ and 2$\frac{A}{3}$. The velocity of liquid at Q is $V_Q$ and Velocity at P is $V_P$ (The cross-sectional area of the main is A)

1. If $V_P$ = 10 m/s, then $V_Q$ = 5 m/s

2. If $V_P$ = 20 m/s, then $V_Q$ = 5 m/s

3. If $V_P$ = 20 m/s, then $V_Q$ = 10 m/s

4. If $V_P$ = 30 m/s, then $V_Q$ = 20 m/s

Q. Water from a tap emerges vertically downwards with an initial speed of $1\text{m/s}$. If the cross-sectional area of tap is ${10}^{-4}{\text{m}}^2$ then find the cross sectional area of stream $0.15\text{m}$ below the tap.

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

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

Q.

In the figure shown, a liquid is flowing through a tube at the rate of 0.1 $m^3$/sec. The tube is randed into two semicircular tubes of cross sectional area $\frac{A}{3}$ and 2$\frac{A}{3}$. The velocity of liquid at Q is $V_Q$ and Velocity at P is $V_P$ (The cross-sectional area of the main is A)

1. If $V_P$ = 10 m/s, then $V_Q$ = 5 m/s

2. If $V_P$ = 20 m/s, then $V_Q$ = 5 m/s

3. If $V_P$ = 20 m/s, then $V_Q$ = 10 m/s

4. If $V_P$ = 30 m/s, then $V_Q$ = 20 m/s

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

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 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.

Water enters through end A with speed $v_1$ and leaves through end B with speed $v_2$ of a cylindrical tube AB. The tube is always completely filled with water. In case I tube is horizontal and in case II it is vertical with end A upwards and in case III it is vertical with end B upwards. We have $v_1$ = $v_2$ for

1. Case I

2. Case II

3. Case III

4. Each case

Q. The cylindrical tube of spray pump has a cross-section of $10{\text{cm}}^2$, one end of which has $50$ fine holes each of area ${10}^{-8}{\text{m}}^2$. If liquid flows inside the tube with a speed of $0.3\text{m/min}$, find the speed with which the liquid is ejected through the holes.

1. $5\text{m/s}$
2. $20\text{m/s}$
3. $10\text{m/s}$
4. $2.5\text{m/s}$

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. 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. $500\text{m/s}$

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.

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. 46 km/hr

2. 23 m/s

3. 23 km/hr

4. 46 m/s

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

Q. The cylindrical tube of a spray pump has a cross-section $5{\text{cm}}^2$, one end of which has $50$ fine holes, each of area ${10}^{-8}{\text{m}}^2$. If the liquid flows inside the tube with a speed of $0.3\text{m/min}$, then find the speed with which the liquid is ejected through the holes.

1. $2\text{m/s}$
2. $5\text{m/s}$
3. $10\text{m/s}$
4. $8\text{m/s}$

Q. The velocity 'v' of the fluid is

1. 3.0 m/s
2. 1.5 m/s
3. 1.0 m/s
4. 2.25 m/s

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

Q. A large open tank has two holes in the wall. One is a square hole of side $2\text{cm}$ at a depth of $5\text{cm}$ from the top and the other is a circular hole of radius $R$ at a depth of $20\text{cm}$ from the top. When the tank is completely filled with water, the quantity of water flowing out per second from both the holes is same. Then, what is the value of $R$?

1. $2\times {10}^{-3}\text{m}$
2. $4\times {10}^{-3}\text{m}$
3. $6\times {10}^{-3}\text{m}$
4. $8\times {10}^{-3}\text{m}$

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

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

Q.

Water flows through a horizontal tube of variable cross section. The area of cross section at A and B are 4 mm² and 2 mm² respectively. If 1 cc of water enters per second through A, find the speed of water at B?

1. 25 cm/s

2. 50 cm/s

3. 25 mm/s

4. 50 mm/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. 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. $500\text{m/s}$