10. Continuity Equation and Bernoulli's Principle and It’s Application
Mechanical Properties of Fluids

143396 A stone is projected vertically up from the bottom of a water tank. Assuming no water resistance it will go up $\&$ come down in same time but if water drag is present then the time it takes to go up, $t_{u p}$ and the time it takes to come down, $t_{\text {down }}$ are related as

1 $t_{\text {up }}>t_{\text {down }}$
2 $t_{\text {up }}=t_{\text {down }}$
3 $t_{\text {up }} \lt t_{\text {down }}$
4 can not say
Mechanical Properties of Fluids

143397 Water flows steadily through a horizontal pipe of a variable cross - section. If the pressure of the water is $p$ at a point, where the speed of the flow is $\mathrm{v}$, what is the pressure at another point, where the speed of the flow is $2 v$ ? Let the density of water be $1 \mathrm{~g}-\mathrm{cm}^{-3}$

1 $p+(3 / 2) \rho v^{2}$
2 $p-2 \rho v^{2}$
3 $p+2 \rho v^{2}$
4 $p-3 \rho v^{2}$
5 $p-(3 / 2) \rho v^{2}$
Mechanical Properties of Fluids

143398 In a horizontal pipe of non-uniform crosssection, water flows with a velocity of $1 \mathrm{~ms}^{-1}$ at a point where the diameter of the pipe in 20 cm. The velocity of water (in $\mathrm{ms}^{-1}$ ) at a point where the diameter of the pipe is $5 \mathbf{c m}$ is

1 64
2 24
3 8
4 32
5 16
Mechanical Properties of Fluids

143402 By sucking through a straw, a student can reduce the pressure in his lungs to $750 \mathrm{~mm}$ of $\mathrm{Hg}\left(\right.$ density $\left.=13.6 \mathrm{~g} / \mathrm{cm}^{3}\right)$. Using the straw, he can drink water from a glass upto a maximum depth of :

1 $10 \mathrm{~cm}$
2 $75 \mathrm{~cm}$
3 $13.6 \mathrm{~cm}$
4 $1.36 \mathrm{~cm}$
Mechanical Properties of Fluids

143403 Water is flowing through a horizontal tube having cross-sectional areas of its two ends being $A$ and $A^{\prime}$ such that the ratio $A / A^{\prime}$ is 5 . If the pressure difference of water between the two ends is $3 \times 10^{5} \mathrm{~N} \mathrm{~m}^{-2}$, the velocity of water with which it enters the tube will be (neglect gravity effects)

1 $5 \mathrm{~m} \mathrm{~s}^{-1}$
2 $10 \mathrm{~m} \mathrm{~s}^{-1}$
3 $25 \mathrm{~m} \mathrm{~s}^{-1}$
4 $50 \sqrt{10} \mathrm{~ms}^{-1}$
Mechanical Properties of Fluids

143396 A stone is projected vertically up from the bottom of a water tank. Assuming no water resistance it will go up $\&$ come down in same time but if water drag is present then the time it takes to go up, $t_{u p}$ and the time it takes to come down, $t_{\text {down }}$ are related as

1 $t_{\text {up }}>t_{\text {down }}$
2 $t_{\text {up }}=t_{\text {down }}$
3 $t_{\text {up }} \lt t_{\text {down }}$
4 can not say
Mechanical Properties of Fluids

143397 Water flows steadily through a horizontal pipe of a variable cross - section. If the pressure of the water is $p$ at a point, where the speed of the flow is $\mathrm{v}$, what is the pressure at another point, where the speed of the flow is $2 v$ ? Let the density of water be $1 \mathrm{~g}-\mathrm{cm}^{-3}$

1 $p+(3 / 2) \rho v^{2}$
2 $p-2 \rho v^{2}$
3 $p+2 \rho v^{2}$
4 $p-3 \rho v^{2}$
5 $p-(3 / 2) \rho v^{2}$
Mechanical Properties of Fluids

143398 In a horizontal pipe of non-uniform crosssection, water flows with a velocity of $1 \mathrm{~ms}^{-1}$ at a point where the diameter of the pipe in 20 cm. The velocity of water (in $\mathrm{ms}^{-1}$ ) at a point where the diameter of the pipe is $5 \mathbf{c m}$ is

1 64
2 24
3 8
4 32
5 16
Mechanical Properties of Fluids

143402 By sucking through a straw, a student can reduce the pressure in his lungs to $750 \mathrm{~mm}$ of $\mathrm{Hg}\left(\right.$ density $\left.=13.6 \mathrm{~g} / \mathrm{cm}^{3}\right)$. Using the straw, he can drink water from a glass upto a maximum depth of :

1 $10 \mathrm{~cm}$
2 $75 \mathrm{~cm}$
3 $13.6 \mathrm{~cm}$
4 $1.36 \mathrm{~cm}$
Mechanical Properties of Fluids

143403 Water is flowing through a horizontal tube having cross-sectional areas of its two ends being $A$ and $A^{\prime}$ such that the ratio $A / A^{\prime}$ is 5 . If the pressure difference of water between the two ends is $3 \times 10^{5} \mathrm{~N} \mathrm{~m}^{-2}$, the velocity of water with which it enters the tube will be (neglect gravity effects)

1 $5 \mathrm{~m} \mathrm{~s}^{-1}$
2 $10 \mathrm{~m} \mathrm{~s}^{-1}$
3 $25 \mathrm{~m} \mathrm{~s}^{-1}$
4 $50 \sqrt{10} \mathrm{~ms}^{-1}$
Mechanical Properties of Fluids

143396 A stone is projected vertically up from the bottom of a water tank. Assuming no water resistance it will go up $\&$ come down in same time but if water drag is present then the time it takes to go up, $t_{u p}$ and the time it takes to come down, $t_{\text {down }}$ are related as

1 $t_{\text {up }}>t_{\text {down }}$
2 $t_{\text {up }}=t_{\text {down }}$
3 $t_{\text {up }} \lt t_{\text {down }}$
4 can not say
Mechanical Properties of Fluids

143397 Water flows steadily through a horizontal pipe of a variable cross - section. If the pressure of the water is $p$ at a point, where the speed of the flow is $\mathrm{v}$, what is the pressure at another point, where the speed of the flow is $2 v$ ? Let the density of water be $1 \mathrm{~g}-\mathrm{cm}^{-3}$

1 $p+(3 / 2) \rho v^{2}$
2 $p-2 \rho v^{2}$
3 $p+2 \rho v^{2}$
4 $p-3 \rho v^{2}$
5 $p-(3 / 2) \rho v^{2}$
Mechanical Properties of Fluids

143398 In a horizontal pipe of non-uniform crosssection, water flows with a velocity of $1 \mathrm{~ms}^{-1}$ at a point where the diameter of the pipe in 20 cm. The velocity of water (in $\mathrm{ms}^{-1}$ ) at a point where the diameter of the pipe is $5 \mathbf{c m}$ is

1 64
2 24
3 8
4 32
5 16
Mechanical Properties of Fluids

143402 By sucking through a straw, a student can reduce the pressure in his lungs to $750 \mathrm{~mm}$ of $\mathrm{Hg}\left(\right.$ density $\left.=13.6 \mathrm{~g} / \mathrm{cm}^{3}\right)$. Using the straw, he can drink water from a glass upto a maximum depth of :

1 $10 \mathrm{~cm}$
2 $75 \mathrm{~cm}$
3 $13.6 \mathrm{~cm}$
4 $1.36 \mathrm{~cm}$
Mechanical Properties of Fluids

143403 Water is flowing through a horizontal tube having cross-sectional areas of its two ends being $A$ and $A^{\prime}$ such that the ratio $A / A^{\prime}$ is 5 . If the pressure difference of water between the two ends is $3 \times 10^{5} \mathrm{~N} \mathrm{~m}^{-2}$, the velocity of water with which it enters the tube will be (neglect gravity effects)

1 $5 \mathrm{~m} \mathrm{~s}^{-1}$
2 $10 \mathrm{~m} \mathrm{~s}^{-1}$
3 $25 \mathrm{~m} \mathrm{~s}^{-1}$
4 $50 \sqrt{10} \mathrm{~ms}^{-1}$
Mechanical Properties of Fluids

143396 A stone is projected vertically up from the bottom of a water tank. Assuming no water resistance it will go up $\&$ come down in same time but if water drag is present then the time it takes to go up, $t_{u p}$ and the time it takes to come down, $t_{\text {down }}$ are related as

1 $t_{\text {up }}>t_{\text {down }}$
2 $t_{\text {up }}=t_{\text {down }}$
3 $t_{\text {up }} \lt t_{\text {down }}$
4 can not say
Mechanical Properties of Fluids

143397 Water flows steadily through a horizontal pipe of a variable cross - section. If the pressure of the water is $p$ at a point, where the speed of the flow is $\mathrm{v}$, what is the pressure at another point, where the speed of the flow is $2 v$ ? Let the density of water be $1 \mathrm{~g}-\mathrm{cm}^{-3}$

1 $p+(3 / 2) \rho v^{2}$
2 $p-2 \rho v^{2}$
3 $p+2 \rho v^{2}$
4 $p-3 \rho v^{2}$
5 $p-(3 / 2) \rho v^{2}$
Mechanical Properties of Fluids

143398 In a horizontal pipe of non-uniform crosssection, water flows with a velocity of $1 \mathrm{~ms}^{-1}$ at a point where the diameter of the pipe in 20 cm. The velocity of water (in $\mathrm{ms}^{-1}$ ) at a point where the diameter of the pipe is $5 \mathbf{c m}$ is

1 64
2 24
3 8
4 32
5 16
Mechanical Properties of Fluids

143402 By sucking through a straw, a student can reduce the pressure in his lungs to $750 \mathrm{~mm}$ of $\mathrm{Hg}\left(\right.$ density $\left.=13.6 \mathrm{~g} / \mathrm{cm}^{3}\right)$. Using the straw, he can drink water from a glass upto a maximum depth of :

1 $10 \mathrm{~cm}$
2 $75 \mathrm{~cm}$
3 $13.6 \mathrm{~cm}$
4 $1.36 \mathrm{~cm}$
Mechanical Properties of Fluids

143403 Water is flowing through a horizontal tube having cross-sectional areas of its two ends being $A$ and $A^{\prime}$ such that the ratio $A / A^{\prime}$ is 5 . If the pressure difference of water between the two ends is $3 \times 10^{5} \mathrm{~N} \mathrm{~m}^{-2}$, the velocity of water with which it enters the tube will be (neglect gravity effects)

1 $5 \mathrm{~m} \mathrm{~s}^{-1}$
2 $10 \mathrm{~m} \mathrm{~s}^{-1}$
3 $25 \mathrm{~m} \mathrm{~s}^{-1}$
4 $50 \sqrt{10} \mathrm{~ms}^{-1}$
Mechanical Properties of Fluids

143396 A stone is projected vertically up from the bottom of a water tank. Assuming no water resistance it will go up $\&$ come down in same time but if water drag is present then the time it takes to go up, $t_{u p}$ and the time it takes to come down, $t_{\text {down }}$ are related as

1 $t_{\text {up }}>t_{\text {down }}$
2 $t_{\text {up }}=t_{\text {down }}$
3 $t_{\text {up }} \lt t_{\text {down }}$
4 can not say
Mechanical Properties of Fluids

143397 Water flows steadily through a horizontal pipe of a variable cross - section. If the pressure of the water is $p$ at a point, where the speed of the flow is $\mathrm{v}$, what is the pressure at another point, where the speed of the flow is $2 v$ ? Let the density of water be $1 \mathrm{~g}-\mathrm{cm}^{-3}$

1 $p+(3 / 2) \rho v^{2}$
2 $p-2 \rho v^{2}$
3 $p+2 \rho v^{2}$
4 $p-3 \rho v^{2}$
5 $p-(3 / 2) \rho v^{2}$
Mechanical Properties of Fluids

143398 In a horizontal pipe of non-uniform crosssection, water flows with a velocity of $1 \mathrm{~ms}^{-1}$ at a point where the diameter of the pipe in 20 cm. The velocity of water (in $\mathrm{ms}^{-1}$ ) at a point where the diameter of the pipe is $5 \mathbf{c m}$ is

1 64
2 24
3 8
4 32
5 16
Mechanical Properties of Fluids

143402 By sucking through a straw, a student can reduce the pressure in his lungs to $750 \mathrm{~mm}$ of $\mathrm{Hg}\left(\right.$ density $\left.=13.6 \mathrm{~g} / \mathrm{cm}^{3}\right)$. Using the straw, he can drink water from a glass upto a maximum depth of :

1 $10 \mathrm{~cm}$
2 $75 \mathrm{~cm}$
3 $13.6 \mathrm{~cm}$
4 $1.36 \mathrm{~cm}$
Mechanical Properties of Fluids

143403 Water is flowing through a horizontal tube having cross-sectional areas of its two ends being $A$ and $A^{\prime}$ such that the ratio $A / A^{\prime}$ is 5 . If the pressure difference of water between the two ends is $3 \times 10^{5} \mathrm{~N} \mathrm{~m}^{-2}$, the velocity of water with which it enters the tube will be (neglect gravity effects)

1 $5 \mathrm{~m} \mathrm{~s}^{-1}$
2 $10 \mathrm{~m} \mathrm{~s}^{-1}$
3 $25 \mathrm{~m} \mathrm{~s}^{-1}$
4 $50 \sqrt{10} \mathrm{~ms}^{-1}$