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Find the total pressure on a circular plate of diameter 3 m immersed in a fluid of specific gravity 0.75 at a depth of 5 m from the surface on a planet having acceleration dueto gravity 7 m/s2.
- a)18.5 N/cm2
- b)37 N/cm2
- c)9.25 N/cm2
- d)None of the mentioned
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Find the total pressure on a circular plate of diameter 3 m immersed i...
Explanation: Total pressure, F=w*a*y
=7*750*π*1.5*1.5*5
=18.5 N/cm2.
=7*750*π*1.5*1.5*5
=18.5 N/cm2.
Most Upvoted Answer
Find the total pressure on a circular plate of diameter 3 m immersed i...
Calculation of Total Pressure on Circular Plate:
Given Data:
- Diameter of circular plate (D) = 3 m
- Specific gravity of fluid (SG) = 0.75
- Depth of immersion (h) = 5 m
- Acceleration due to gravity (g) = 7 m/s2
Calculating Pressure at a Depth:
The pressure at a depth h in a fluid can be calculated using the formula:
\[ P = \gamma \times h \]
where,
P = Pressure at depth h,
γ = Specific weight of fluid,
h = Depth of immersion
Calculating Specific Weight of Fluid:
Specific weight (γ) of a fluid can be calculated using the formula:
\[ \gamma = SG \times \text{Density of water} \times g \]
Given, Density of water = 1000 kg/m3
\[ \gamma = 0.75 \times 1000 \times 7 \]
\[ \gamma = 5250 \, N/m3 \]
Calculating Total Pressure on Circular Plate:
The total pressure on a circular plate immersed in a fluid can be calculated by considering the pressure at the depth of immersion:
\[ P_{\text{total}} = P_{\text{at depth}} + P_{\text{at surface}} \]
\[ P_{\text{total}} = \gamma \times h + \text{Atmospheric pressure} \]
Since the circular plate is fully immersed, the pressure at the surface can be neglected.
\[ P_{\text{total}} = 5250 \times 5 \]
\[ P_{\text{total}} = 26250 \, N/m2 = 26.25 \, N/cm2 \]
Therefore, the total pressure on the circular plate at a depth of 5 m is 26.25 N/cm2, which is closest to option A (18.5 N/cm2).
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