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In a stationary fluid, how do the local pressure of the fluid vary?
- a)With depth only
- b)In the horizontal direction only
- c)Both with depth and along horizontal direction
- d)Neither with depth nor along horizontal direction
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
In a stationary fluid, how do the local pressure of the fluid vary?a)...
According to Pascal’s law, the local pressure of a fluid is same in all directions. Hence, the pressure won’t vary along the x and y-direction. The local pressure will increase with an increase in depth due to the extra weight of water column above that point.
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Community Answer
In a stationary fluid, how do the local pressure of the fluid vary?a)...
In a stationary fluid, how do the local pressure of the fluid vary?
The local pressure of a fluid in a stationary state can vary with depth only. This is due to the hydrostatic pressure distribution in the fluid, which is primarily influenced by the gravitational force acting on the fluid.
Explanation:
Hydrostatic Pressure:
Hydrostatic pressure is the pressure exerted by a fluid at a given point within itself. It arises due to the weight of the fluid above that point. In a stationary fluid, the hydrostatic pressure varies with depth and is independent of the horizontal direction.
Pressure Variation with Depth:
When we consider a fluid column of height 'h' at rest, the pressure at the bottom of the column is greater than the pressure at the top due to the weight of the fluid above. This pressure difference is given by the equation:
ΔP = ρgh
Where ΔP is the pressure difference, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height or depth of the fluid column.
Pressure Variation along Horizontal Direction:
In a stationary fluid, the pressure does not vary along the horizontal direction. This is because the fluid is at rest, and there are no shearing forces or velocity gradients in the fluid. Therefore, the pressure remains constant in the horizontal direction.
Conclusion:
In summary, the local pressure of a stationary fluid varies only with depth. The pressure increases with depth due to the weight of the fluid above, following the hydrostatic pressure distribution. However, the pressure remains constant along the horizontal direction as there are no shearing forces or velocity gradients in the fluid.
The local pressure of a fluid in a stationary state can vary with depth only. This is due to the hydrostatic pressure distribution in the fluid, which is primarily influenced by the gravitational force acting on the fluid.
Explanation:
Hydrostatic Pressure:
Hydrostatic pressure is the pressure exerted by a fluid at a given point within itself. It arises due to the weight of the fluid above that point. In a stationary fluid, the hydrostatic pressure varies with depth and is independent of the horizontal direction.
Pressure Variation with Depth:
When we consider a fluid column of height 'h' at rest, the pressure at the bottom of the column is greater than the pressure at the top due to the weight of the fluid above. This pressure difference is given by the equation:
ΔP = ρgh
Where ΔP is the pressure difference, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height or depth of the fluid column.
Pressure Variation along Horizontal Direction:
In a stationary fluid, the pressure does not vary along the horizontal direction. This is because the fluid is at rest, and there are no shearing forces or velocity gradients in the fluid. Therefore, the pressure remains constant in the horizontal direction.
Conclusion:
In summary, the local pressure of a stationary fluid varies only with depth. The pressure increases with depth due to the weight of the fluid above, following the hydrostatic pressure distribution. However, the pressure remains constant along the horizontal direction as there are no shearing forces or velocity gradients in the fluid.
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