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Calculate the hydrostatic pressure for water moving with constant velocity at a depth of 5 m from the surface.
- a)49 kN/m2
- b)98 kN/m2
- c)since fluid is in motion, we cannot analyse
- d)None of the mentioned
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Calculate the hydrostatic pressure for water moving with constant velo...
Explanation: If fluid is moving with uniform velocity we treat it analytically same as if fluid is at rest
p= ρgh.
p= ρgh.
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Calculate the hydrostatic pressure for water moving with constant velo...
Calculation of Hydrostatic Pressure for Water:
- Hydrostatic pressure is the pressure exerted by a fluid at rest, due to the weight of the fluid.
- It is given by the formula P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity and h is the depth of the fluid.
- In this case, water is moving with constant velocity at a depth of 5 m from the surface.
- Since the water is at rest with respect to the moving frame of reference, we can assume that the water is at rest and use the formula for hydrostatic pressure.
- The density of water is 1000 kg/m³ and the acceleration due to gravity is 9.81 m/s².
- Substituting these values in the formula, we get P = 1000 x 9.81 x 5 = 49,050 Pa.
- Converting this to kN/m², we get 49 kN/m².
- Therefore, the correct answer is option A.
Note: The assumption that the water is at rest with respect to the moving frame of reference may not always be valid. In such cases, the pressure would be a combination of hydrostatic pressure and dynamic pressure, and cannot be calculated using the formula for hydrostatic pressure alone.
- Hydrostatic pressure is the pressure exerted by a fluid at rest, due to the weight of the fluid.
- It is given by the formula P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity and h is the depth of the fluid.
- In this case, water is moving with constant velocity at a depth of 5 m from the surface.
- Since the water is at rest with respect to the moving frame of reference, we can assume that the water is at rest and use the formula for hydrostatic pressure.
- The density of water is 1000 kg/m³ and the acceleration due to gravity is 9.81 m/s².
- Substituting these values in the formula, we get P = 1000 x 9.81 x 5 = 49,050 Pa.
- Converting this to kN/m², we get 49 kN/m².
- Therefore, the correct answer is option A.
Note: The assumption that the water is at rest with respect to the moving frame of reference may not always be valid. In such cases, the pressure would be a combination of hydrostatic pressure and dynamic pressure, and cannot be calculated using the formula for hydrostatic pressure alone.
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