Obtain Bernoulli’s equation for steady, incompressible, irrotational and viscous liquid.
Obtain Bernoulli’s equation for steady, incompressible, irrotational and viscous liquid.
A pipe is shown in figure.
At point B of left end of pipe
$\rightarrow$ Fluid speed $=v_{1}$
$\rightarrow$ Cross sectional area $=\mathrm{A}_{1} .$
$\rightarrow$ Pressure exerted on fluid $\mathrm{P}_{1}=\frac{\mathrm{F}_{1}}{\mathrm{~A}_{1}}$
At point $D$, of right end of pipe,
$\rightarrow$ Fluid speed $=v_{2}$
$\rightarrow$ Cross sectional area $=\mathrm{A}_{2}$
$\rightarrow$ Pressure exerted on the fluid $\mathrm{P}_{2}=\frac{\mathrm{F}_{2}}{\mathrm{~A}_{2}}$.
Force $\mathrm{F}_{1}=\mathrm{P}_{1} \mathrm{~A}_{1}$ exerted on fluid at point $\mathrm{B}$, covers distance
done on fluid
$\mathrm{W}_{1} =(\text { Force }) \text { (displacement) }$
$\mathrm{W}_{1} =\mathrm{P}_{1} \mathrm{~A}_{1} v_{1} \Delta t$
$\therefore \mathrm{W}_{1} =\mathrm{P}_{1}\left(\Delta \mathrm{V}_{1}\right)$
(where $\Delta \mathrm{V}=\mathrm{A}_{1} v_{1} \Delta t=$ volume of fluid)
Similar Questions
The platelets are drifting with the blood flowing in a streamline flow through a horizontal artery as shown below Artery is contracted in region $II$. Choose the correct statement.
The platelets are drifting with the blood flowing in a streamline flow through a horizontal artery as shown below Artery is contracted in region $II$. Choose the correct statement.
- [KVPY 2020]
Fig. represents vertical sections of four wings moving horizontally in air. In which case the force is upwards
Fig. represents vertical sections of four wings moving horizontally in air. In which case the force is upwards
Consider a water tank as shown in the figure. It's cross-sectional area is $0.4\, m ^{2}$. The tank has an opening $B$ near the bottom whose cross-section area is $1\, cm ^{2}$. A load of $24\, kg$ is applied on the water at the top when the height of the water level is $40\, cm$ above the bottom, the velocity of water coming out the opening $B$ is $v\, ms ^{-1}$. The value of $v$, to the nearest integer, is ......$m/s$. [Take value of $g$ to be $10 \,ms ^{-2}$ ]
Consider a water tank as shown in the figure. It's cross-sectional area is $0.4\, m ^{2}$. The tank has an opening $B$ near the bottom whose cross-section area is $1\, cm ^{2}$. A load of $24\, kg$ is applied on the water at the top when the height of the water level is $40\, cm$ above the bottom, the velocity of water coming out the opening $B$ is $v\, ms ^{-1}$. The value of $v$, to the nearest integer, is ......$m/s$. [Take value of $g$ to be $10 \,ms ^{-2}$ ]
- [JEE MAIN 2021]
A manometer connected to a closed tap reads $4.5 \times {10^5}$ pascal. When the tap is opened the reading of the manometer falls to $4 \times {10^5}$ pascal. Then the velocity of flow of water is ........ $m{s^{ - 1}}$
A manometer connected to a closed tap reads $4.5 \times {10^5}$ pascal. When the tap is opened the reading of the manometer falls to $4 \times {10^5}$ pascal. Then the velocity of flow of water is ........ $m{s^{ - 1}}$
What is a venturi-meter ? Explain its construction and working.
What is a venturi-meter ? Explain its construction and working.