Write the expression for computing the pressure in a fluid.
Expression of pressure in a fluid
Explanation of Solution
Given:-
Density of fluid and depth of fluid.
In a fluid, if the fluid is stationary, the state of pressure at a point may be defined using pascal's law and hydrostatic law.
According to pascal's law, In a fluid, at a particular point, pressure acts uniformly and is equal in all the directions.
Resolving the forces in x direction,
Resolving the pressure forces in the y direction
Since the choice of fluid element is arbitrary, force on BC could be in any direction, Hence pressure at a point in all the direction is uniform and is equal in all direction.
The hydrostatic law states that the rate of increase with respect to depth in a stationary fluid is equal to the specific weight of the fluid.
To prove this, consider a small rectangular shaped fluid element of cross sectional area
further at a given depth in a fluid, for a given density,
specific weight, w=
Hence to find the value of pressure at any depth Z, integrate both sides of eq2
Conclusion:
Pressure, P=
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