H C Verma Solutions for Chapter: Fluid Mechanics, Exercise 4: EXERCISES

Water flows through a horizontal tube of variable cross-section (figure). The area of the cross-section at $A$ and $B$ are $4 {\mathrm{mm}}^2$ and $2 {\mathrm{mm}}^2$, respectively. If $1 \mathrm{cc}$ of water enters per second through $A$, find $\left(a\right)$ the speed of the water at $A$, $\left(b\right)$ the speed of the water at $B$ and
$\left(c\right)$ the pressure difference $P_{\mathrm{A}}-P_{\mathrm{B}}$.

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Water flows through a horizontal tube of variable cross-section (figure). The area of the cross-section at $\mathrm{A}$ and $\mathrm{B}$ are $4 {\mathrm{mm}}^2$ and $2 {\mathrm{mm}}^2$, respectively. $1 \mathrm{cc}$ of water enters per second through $\mathrm{A}$. If the tube is kept vertical with $\mathrm{A}$ upward but the other conditions remain the same, the separation between the cross-sections at $\mathrm{A}$ and $\mathrm{B}$ is $\frac{15}{16} \mathrm{cm}$. Find $\left(a\right)$ the speed of the water at $\mathrm{A}$, $\left(b\right)$ the speed of the water at $\mathrm{B}$ and $\left(c\right)$ the pressure difference $P_{\mathrm{A}}-P_{\mathrm{B}}$. Take $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$.

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Water flows through a horizontal tube of variable cross-section(figure). The area of the cross-section at $\mathrm{A}$ and $\mathrm{B}$ are $4 {\mathrm{mm}}^2$ and $2 {\mathrm{mm}}^2$, respectively. If the tube is kept vertical with $\mathrm{B}$ upward, the separation between the cross-sections at $\mathrm{A}$ and $\mathrm{B}$ is $\frac{15}{16} \mathrm{cm}$. Water enters through $\mathrm{B}$ at the rate of $1 {\mathrm{cm}}^3 {\mathrm{s}}^{-1}$. Find $\left(a\right)$ the speed of water at $\mathrm{A}$, $\left(b\right)$ the speed of water at $\mathrm{B}$ and $\left(c\right)$ the pressure difference $P_{\mathrm{A}}-P_{\mathrm{B}}$. Take $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$.
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Water flows through a tube, as shown in the figure. The areas of the cross-section at $A$ and $B$ are $1 {\mathrm{cm}}^2$ and $0.5 {\mathrm{cm}}^2$, respectively. The height difference between $A$ and $B$ is $5 \mathrm{cm}$. If the speed of the water at $A$ is $10 \mathrm{cm} {\mathrm{s}}^{-1}$, find $\left(a\right)$ the speed at $B$ and $\left(b\right)$ the difference in pressures at $A$ and $B$

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Water flows through a horizontal tube, as shown in the figure. If the difference of heights of the water column in the vertical tubes is $2 \mathrm{cm}$ and the areas of the cross-section at $A$ and $B$ are $4 {\mathrm{cm}}^2$ and $2 {\mathrm{cm}}^2$, respectively, find the rate of flow of water across any section.

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Water flows through the tube, as shown in the figure. The areas of the cross-section of the wide and the narrow portions of the tube are $5 {\mathrm{cm}}^2$ and $2 {\mathrm{cm}}^2$, respectively. The rate of flow of water through the tube is $500 {\mathrm{cm}}^3 {\mathrm{s}}^{-1}$. Find the difference in the mercury levels in the $\mathrm{U}$-tube.

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Water leaks out from an open tank through a hole in the area $2 {\mathrm{mm}}^2$ at the bottom. Suppose water is filled up to a height of $80 \mathrm{cm}$ and the area of cross-section of the tank is $0.4 {\mathrm{m}}^2$. The pressure at the open surface and at the hole is equal to the atmospheric pressure. Neglect the small velocity of the water near the open surface in the tank.
$\left(a\right)$ Find the initial speed of water coming out of the hole.
$\left(b\right)$ Find the speed of water coming out when half of the water has leaked out.
$\left(c\right)$ Find the volume of water leaked out during a time interval $dt$ after the height remained is $h$. Thus, find a decrease in height $\mathrm{d}h$ in terms of $h$ and $\mathrm{d}t$.
$\left(d\right)$ From the result of part $\left(c\right)$, find the time required for half of the water to leak out.

The water level is maintained in a cylindrical vessel up to a fixed height $H$. The vessel is kept on a horizontal plane. At what height above the bottom should a hole be made in the vessel, so that the water stream coming out of the hole strikes the horizontal plane at the greatest distance from the vessel?

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