Equation of Continuity

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. Length of the tube of the flow and velocity of the liquid
3. Volume of the tube of the flow and velocity of the liquid
4. Viscous force acting on the liquid layer and velocity of the liquid

Q. In the given figure, the velocity $v_3$ will be

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

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 flow of liquid in which its layer slides over another without mixing, is called

1. Ideal Flow

2. Non-viscous flow

3. Laminar flow

4. Turbulent flow

Q. 51. What should be the average velocity of water in a tube of radius 2.5 mm so that the flow is just turbulent.? Viscosity of water is 0.001 pa 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. 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 tube has two areas of cross-section as shown in the figure. The diameter of the bigger section is double the diameter of the smaller section. Find the range of water falling on the horizontal surface, if piston is moving with a constant velocity $0.4\text{m/s}$ and $h=2.5\text{m}(g=10{\text{m/s}}^2)$

1. $1.13\text{m}$
2. $1.5\text{m}$
3. $2\text{m}$
4. $1.51\text{m}$

Q.

what is the unit of reynolds number and give its value?

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. 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. The cylindrical tube of a spray pump has a cross-section of 8.0 cm2 one end of which has 40 fine holes each of diameter 1.0 mm. If the liquid flow inside the tube is 1.5 m min¯¹, what is the speed of ejection of the liquid through the holes ?

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. An incompressible liquid flows through a horizontal tube as shown in the following fig. Then the velocity v of the fluid is

1. 
   
2. 
   
3. 
   
4. 
   

Q. Calculate the speed (in $\text{mm/s}$) of flow of glycerin at the inlet of the conical section of a pipe. If its inlet and outlet radius are $0.2\text{m}$ and $0.05\text{m}$ respectively. The pressure drop across its length is $10{\text{N/m}}^2$ and density of glycerin is $1.25\times {10}^3{\text{kg/m}}^3$.

1. $64.4$
2. $32.6$
3. $10$
4. $2.6$

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.

An incompressible liquid flows through a horizontal tube as shown in the following fig. Then 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 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.

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. 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. Dimensions of rate of Flow

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

Q.

Water flows through two identical tubes A and B. A volume V₀ of water passes through the tube A and 2 V₀ through B in a given time. Which of the following may be correct?

1. Flow in both the tubes are steady.

2. Flow is steady in B but turbulent in A.

3. Flow in both the tubes are turbulent.

4. Flow is steady in A but turbulent in A.

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. 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.

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.

state the equation of continuity

Q. The principle of continuity is consequence of

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

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

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