06. Flow of Fluid
Mechanical Properties of Fluids

143282 As per a popular Hini movi, the people from a small village are trying to set up their own small hydroelectric power station capable of generating a power of $90 \mathrm{~kW}$. The water reservoir used for this purpose is located on a hilltop at a height of $h$ meter from the ground and it can hold $v$ liter of water. The water from the reservoir rushes to the ground through some pipes and rotates the blades of a turbine connected with the generator. If $\rho$ is the density of water and the efficiency of the machine is $\mathbf{9 0} \%$, then the rate at which the water must flow through the pipe will be

1 $\frac{10^{5}}{\rho g h}$
2 $\frac{10^{4}}{\rho g h}$
3 $\frac{10^{3}}{\rho g h}$
4 None of the above
Mechanical Properties of Fluids

143283 A U-tube open at both the ends is partially filled with a liquid (A) of density $950 \mathrm{kgm}^{-3}$. Another liquid (B) of density $820 \mathrm{kgm}^{-3}$ is poured into one of the arms and it forms a column of length $10 \mathrm{~cm}$ as shown in the figure. If the arm into which liquid $B$ is poured is shielded from any air motion, the speed with which air should be blown across the top of the other arm till the levels of the two liquids are at same height in $\mathrm{ms}^{-1}$ is (Density of air is $1.3 \mathrm{kgm}^{-3}$. Acceleration due to gravity $=9.8 \mathrm{~ms}^{-2}$ )

1 3.5
2 7
3 14
4 21
Mechanical Properties of Fluids

143284 Match the following List-I with the List-II List-I List-II
| | List-I | List-II |
| :--- | :--- | :--- |
|(A) | Equation of continuity | (I) Less than critical Velocity |
|(B) | Bernoulli's | (II) Formation of eddies and vo |
|(C) |Turbulent flow |(III) Law of conservation of mass|
|(D) |Stream line flow |(IV) Law of conservation of energy|
The correct answer is

1 IV (A) II (B) I (C) III (D)
2 III (A) I (B) IV (C) II (D)
3 II (A) III (B) IV (C) I (D)
4 III (A) IV (B) II (C) I (D)
Mechanical Properties of Fluids

143285 A cylindrical tank having large diameter is filled with water to a height $H$. A hole of crosssectional area $5 \mathrm{~cm}^{2}$ in the tank allows water to drain out. If the water drains out at the rate of $2 \times 10^{-3} \mathrm{~m}^{3} \mathrm{~s}^{-1}$. Then the value of $\mathrm{H}$ is (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

1 $80 \mathrm{~cm}$
2 $120 \mathrm{~cm}$
3 $60 \mathrm{~cm}$
4 $90 \mathrm{~cm}$
Mechanical Properties of Fluids

143286 Consider two liquids $A$ and $B$ in a $U$-shaped tube in static equilibrium as shown in the figure. If the density of the liquid $A$ is twice the density of liquid $B$, the relation between $h_{A}$ and $\mathbf{h}_{B}$ is

1 $\mathrm{h}_{\mathrm{A}}=\frac{\mathrm{h}_{\mathrm{B}}}{\sqrt{2}}$
2 $\mathrm{h}_{\mathrm{A}}=\frac{\mathrm{h}_{\mathrm{B}}}{2}$
3 $\mathrm{h}_{\mathrm{A}}=\frac{\mathrm{h}_{\mathrm{B}}}{3}$
4 $\mathrm{h}_{\mathrm{A}}=\frac{\mathrm{h}_{\mathrm{B}}}{\sqrt{3}}$
Mechanical Properties of Fluids

143282 As per a popular Hini movi, the people from a small village are trying to set up their own small hydroelectric power station capable of generating a power of $90 \mathrm{~kW}$. The water reservoir used for this purpose is located on a hilltop at a height of $h$ meter from the ground and it can hold $v$ liter of water. The water from the reservoir rushes to the ground through some pipes and rotates the blades of a turbine connected with the generator. If $\rho$ is the density of water and the efficiency of the machine is $\mathbf{9 0} \%$, then the rate at which the water must flow through the pipe will be

1 $\frac{10^{5}}{\rho g h}$
2 $\frac{10^{4}}{\rho g h}$
3 $\frac{10^{3}}{\rho g h}$
4 None of the above
Mechanical Properties of Fluids

143283 A U-tube open at both the ends is partially filled with a liquid (A) of density $950 \mathrm{kgm}^{-3}$. Another liquid (B) of density $820 \mathrm{kgm}^{-3}$ is poured into one of the arms and it forms a column of length $10 \mathrm{~cm}$ as shown in the figure. If the arm into which liquid $B$ is poured is shielded from any air motion, the speed with which air should be blown across the top of the other arm till the levels of the two liquids are at same height in $\mathrm{ms}^{-1}$ is (Density of air is $1.3 \mathrm{kgm}^{-3}$. Acceleration due to gravity $=9.8 \mathrm{~ms}^{-2}$ )

1 3.5
2 7
3 14
4 21
Mechanical Properties of Fluids

143284 Match the following List-I with the List-II List-I List-II
| | List-I | List-II |
| :--- | :--- | :--- |
|(A) | Equation of continuity | (I) Less than critical Velocity |
|(B) | Bernoulli's | (II) Formation of eddies and vo |
|(C) |Turbulent flow |(III) Law of conservation of mass|
|(D) |Stream line flow |(IV) Law of conservation of energy|
The correct answer is

1 IV (A) II (B) I (C) III (D)
2 III (A) I (B) IV (C) II (D)
3 II (A) III (B) IV (C) I (D)
4 III (A) IV (B) II (C) I (D)
Mechanical Properties of Fluids

143285 A cylindrical tank having large diameter is filled with water to a height $H$. A hole of crosssectional area $5 \mathrm{~cm}^{2}$ in the tank allows water to drain out. If the water drains out at the rate of $2 \times 10^{-3} \mathrm{~m}^{3} \mathrm{~s}^{-1}$. Then the value of $\mathrm{H}$ is (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

1 $80 \mathrm{~cm}$
2 $120 \mathrm{~cm}$
3 $60 \mathrm{~cm}$
4 $90 \mathrm{~cm}$
Mechanical Properties of Fluids

143286 Consider two liquids $A$ and $B$ in a $U$-shaped tube in static equilibrium as shown in the figure. If the density of the liquid $A$ is twice the density of liquid $B$, the relation between $h_{A}$ and $\mathbf{h}_{B}$ is

1 $\mathrm{h}_{\mathrm{A}}=\frac{\mathrm{h}_{\mathrm{B}}}{\sqrt{2}}$
2 $\mathrm{h}_{\mathrm{A}}=\frac{\mathrm{h}_{\mathrm{B}}}{2}$
3 $\mathrm{h}_{\mathrm{A}}=\frac{\mathrm{h}_{\mathrm{B}}}{3}$
4 $\mathrm{h}_{\mathrm{A}}=\frac{\mathrm{h}_{\mathrm{B}}}{\sqrt{3}}$
Mechanical Properties of Fluids

143282 As per a popular Hini movi, the people from a small village are trying to set up their own small hydroelectric power station capable of generating a power of $90 \mathrm{~kW}$. The water reservoir used for this purpose is located on a hilltop at a height of $h$ meter from the ground and it can hold $v$ liter of water. The water from the reservoir rushes to the ground through some pipes and rotates the blades of a turbine connected with the generator. If $\rho$ is the density of water and the efficiency of the machine is $\mathbf{9 0} \%$, then the rate at which the water must flow through the pipe will be

1 $\frac{10^{5}}{\rho g h}$
2 $\frac{10^{4}}{\rho g h}$
3 $\frac{10^{3}}{\rho g h}$
4 None of the above
Mechanical Properties of Fluids

143283 A U-tube open at both the ends is partially filled with a liquid (A) of density $950 \mathrm{kgm}^{-3}$. Another liquid (B) of density $820 \mathrm{kgm}^{-3}$ is poured into one of the arms and it forms a column of length $10 \mathrm{~cm}$ as shown in the figure. If the arm into which liquid $B$ is poured is shielded from any air motion, the speed with which air should be blown across the top of the other arm till the levels of the two liquids are at same height in $\mathrm{ms}^{-1}$ is (Density of air is $1.3 \mathrm{kgm}^{-3}$. Acceleration due to gravity $=9.8 \mathrm{~ms}^{-2}$ )

1 3.5
2 7
3 14
4 21
Mechanical Properties of Fluids

143284 Match the following List-I with the List-II List-I List-II
| | List-I | List-II |
| :--- | :--- | :--- |
|(A) | Equation of continuity | (I) Less than critical Velocity |
|(B) | Bernoulli's | (II) Formation of eddies and vo |
|(C) |Turbulent flow |(III) Law of conservation of mass|
|(D) |Stream line flow |(IV) Law of conservation of energy|
The correct answer is

1 IV (A) II (B) I (C) III (D)
2 III (A) I (B) IV (C) II (D)
3 II (A) III (B) IV (C) I (D)
4 III (A) IV (B) II (C) I (D)
Mechanical Properties of Fluids

143285 A cylindrical tank having large diameter is filled with water to a height $H$. A hole of crosssectional area $5 \mathrm{~cm}^{2}$ in the tank allows water to drain out. If the water drains out at the rate of $2 \times 10^{-3} \mathrm{~m}^{3} \mathrm{~s}^{-1}$. Then the value of $\mathrm{H}$ is (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

1 $80 \mathrm{~cm}$
2 $120 \mathrm{~cm}$
3 $60 \mathrm{~cm}$
4 $90 \mathrm{~cm}$
Mechanical Properties of Fluids

143286 Consider two liquids $A$ and $B$ in a $U$-shaped tube in static equilibrium as shown in the figure. If the density of the liquid $A$ is twice the density of liquid $B$, the relation between $h_{A}$ and $\mathbf{h}_{B}$ is

1 $\mathrm{h}_{\mathrm{A}}=\frac{\mathrm{h}_{\mathrm{B}}}{\sqrt{2}}$
2 $\mathrm{h}_{\mathrm{A}}=\frac{\mathrm{h}_{\mathrm{B}}}{2}$
3 $\mathrm{h}_{\mathrm{A}}=\frac{\mathrm{h}_{\mathrm{B}}}{3}$
4 $\mathrm{h}_{\mathrm{A}}=\frac{\mathrm{h}_{\mathrm{B}}}{\sqrt{3}}$
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Mechanical Properties of Fluids

143282 As per a popular Hini movi, the people from a small village are trying to set up their own small hydroelectric power station capable of generating a power of $90 \mathrm{~kW}$. The water reservoir used for this purpose is located on a hilltop at a height of $h$ meter from the ground and it can hold $v$ liter of water. The water from the reservoir rushes to the ground through some pipes and rotates the blades of a turbine connected with the generator. If $\rho$ is the density of water and the efficiency of the machine is $\mathbf{9 0} \%$, then the rate at which the water must flow through the pipe will be

1 $\frac{10^{5}}{\rho g h}$
2 $\frac{10^{4}}{\rho g h}$
3 $\frac{10^{3}}{\rho g h}$
4 None of the above
Mechanical Properties of Fluids

143283 A U-tube open at both the ends is partially filled with a liquid (A) of density $950 \mathrm{kgm}^{-3}$. Another liquid (B) of density $820 \mathrm{kgm}^{-3}$ is poured into one of the arms and it forms a column of length $10 \mathrm{~cm}$ as shown in the figure. If the arm into which liquid $B$ is poured is shielded from any air motion, the speed with which air should be blown across the top of the other arm till the levels of the two liquids are at same height in $\mathrm{ms}^{-1}$ is (Density of air is $1.3 \mathrm{kgm}^{-3}$. Acceleration due to gravity $=9.8 \mathrm{~ms}^{-2}$ )

1 3.5
2 7
3 14
4 21
Mechanical Properties of Fluids

143284 Match the following List-I with the List-II List-I List-II
| | List-I | List-II |
| :--- | :--- | :--- |
|(A) | Equation of continuity | (I) Less than critical Velocity |
|(B) | Bernoulli's | (II) Formation of eddies and vo |
|(C) |Turbulent flow |(III) Law of conservation of mass|
|(D) |Stream line flow |(IV) Law of conservation of energy|
The correct answer is

1 IV (A) II (B) I (C) III (D)
2 III (A) I (B) IV (C) II (D)
3 II (A) III (B) IV (C) I (D)
4 III (A) IV (B) II (C) I (D)
Mechanical Properties of Fluids

143285 A cylindrical tank having large diameter is filled with water to a height $H$. A hole of crosssectional area $5 \mathrm{~cm}^{2}$ in the tank allows water to drain out. If the water drains out at the rate of $2 \times 10^{-3} \mathrm{~m}^{3} \mathrm{~s}^{-1}$. Then the value of $\mathrm{H}$ is (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

1 $80 \mathrm{~cm}$
2 $120 \mathrm{~cm}$
3 $60 \mathrm{~cm}$
4 $90 \mathrm{~cm}$
Mechanical Properties of Fluids

143286 Consider two liquids $A$ and $B$ in a $U$-shaped tube in static equilibrium as shown in the figure. If the density of the liquid $A$ is twice the density of liquid $B$, the relation between $h_{A}$ and $\mathbf{h}_{B}$ is

1 $\mathrm{h}_{\mathrm{A}}=\frac{\mathrm{h}_{\mathrm{B}}}{\sqrt{2}}$
2 $\mathrm{h}_{\mathrm{A}}=\frac{\mathrm{h}_{\mathrm{B}}}{2}$
3 $\mathrm{h}_{\mathrm{A}}=\frac{\mathrm{h}_{\mathrm{B}}}{3}$
4 $\mathrm{h}_{\mathrm{A}}=\frac{\mathrm{h}_{\mathrm{B}}}{\sqrt{3}}$
Mechanical Properties of Fluids

143282 As per a popular Hini movi, the people from a small village are trying to set up their own small hydroelectric power station capable of generating a power of $90 \mathrm{~kW}$. The water reservoir used for this purpose is located on a hilltop at a height of $h$ meter from the ground and it can hold $v$ liter of water. The water from the reservoir rushes to the ground through some pipes and rotates the blades of a turbine connected with the generator. If $\rho$ is the density of water and the efficiency of the machine is $\mathbf{9 0} \%$, then the rate at which the water must flow through the pipe will be

1 $\frac{10^{5}}{\rho g h}$
2 $\frac{10^{4}}{\rho g h}$
3 $\frac{10^{3}}{\rho g h}$
4 None of the above
Mechanical Properties of Fluids

143283 A U-tube open at both the ends is partially filled with a liquid (A) of density $950 \mathrm{kgm}^{-3}$. Another liquid (B) of density $820 \mathrm{kgm}^{-3}$ is poured into one of the arms and it forms a column of length $10 \mathrm{~cm}$ as shown in the figure. If the arm into which liquid $B$ is poured is shielded from any air motion, the speed with which air should be blown across the top of the other arm till the levels of the two liquids are at same height in $\mathrm{ms}^{-1}$ is (Density of air is $1.3 \mathrm{kgm}^{-3}$. Acceleration due to gravity $=9.8 \mathrm{~ms}^{-2}$ )

1 3.5
2 7
3 14
4 21
Mechanical Properties of Fluids

143284 Match the following List-I with the List-II List-I List-II
| | List-I | List-II |
| :--- | :--- | :--- |
|(A) | Equation of continuity | (I) Less than critical Velocity |
|(B) | Bernoulli's | (II) Formation of eddies and vo |
|(C) |Turbulent flow |(III) Law of conservation of mass|
|(D) |Stream line flow |(IV) Law of conservation of energy|
The correct answer is

1 IV (A) II (B) I (C) III (D)
2 III (A) I (B) IV (C) II (D)
3 II (A) III (B) IV (C) I (D)
4 III (A) IV (B) II (C) I (D)
Mechanical Properties of Fluids

143285 A cylindrical tank having large diameter is filled with water to a height $H$. A hole of crosssectional area $5 \mathrm{~cm}^{2}$ in the tank allows water to drain out. If the water drains out at the rate of $2 \times 10^{-3} \mathrm{~m}^{3} \mathrm{~s}^{-1}$. Then the value of $\mathrm{H}$ is (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

1 $80 \mathrm{~cm}$
2 $120 \mathrm{~cm}$
3 $60 \mathrm{~cm}$
4 $90 \mathrm{~cm}$
Mechanical Properties of Fluids

143286 Consider two liquids $A$ and $B$ in a $U$-shaped tube in static equilibrium as shown in the figure. If the density of the liquid $A$ is twice the density of liquid $B$, the relation between $h_{A}$ and $\mathbf{h}_{B}$ is

1 $\mathrm{h}_{\mathrm{A}}=\frac{\mathrm{h}_{\mathrm{B}}}{\sqrt{2}}$
2 $\mathrm{h}_{\mathrm{A}}=\frac{\mathrm{h}_{\mathrm{B}}}{2}$
3 $\mathrm{h}_{\mathrm{A}}=\frac{\mathrm{h}_{\mathrm{B}}}{3}$
4 $\mathrm{h}_{\mathrm{A}}=\frac{\mathrm{h}_{\mathrm{B}}}{\sqrt{3}}$