UPSC Exam > UPSC Questions > Question: A house-top water tank is made of f...
Start Learning for Free
Question: A house-top water tank is made of flat plates and is full to the brim. Its height is twice that of any side. The ratio of total thrust force on the bottom of the tank to that on any side will be:
Doubt:
on everywhere it's answer is showing 1.
while calculating the vertical side they have considered average by assuming uniform pressure which is not mentioned in Question. Kindly help with it.
Why are we taking height of centre pressure as h/2, why not {h/2+ MOI/A. h/2}.?
Doubt:
on everywhere it's answer is showing 1.
while calculating the vertical side they have considered average by assuming uniform pressure which is not mentioned in Question. Kindly help with it.
Why are we taking height of centre pressure as h/2, why not {h/2+ MOI/A. h/2}.?
Most Upvoted Answer
Question: A house-top water tank is made of flat plates and is full to...
Understanding Thrust Force in a Water Tank
To analyze the thrust force on the bottom of the tank and on its sides, we need to consider the principles of fluid mechanics.
Thrust Force on the Bottom of the Tank
- The total thrust force on the bottom is calculated using the formula:
Thrust Force = Pressure × Area
- The pressure at the bottom of the tank is determined by the height of the water column (h). Since the tank is full, the pressure at the bottom is given by:
Pressure = ρgh (where ρ is the density of water and g is the acceleration due to gravity).
Thrust Force on the Sides of the Tank
- The thrust force on the vertical sides of the tank varies with depth due to hydrostatic pressure.
- The average pressure on a side is considered to calculate the total thrust force. The average height of the center of pressure is located at h/2 from the top, not accounting for the moment of inertia (MOI) since the average pressure gives us a simplified view.
Ratio of Forces
- The ratio of the total thrust force on the bottom of the tank to that on any side is derived as follows:
- Bottom thrust force is proportional to h.
- Side thrust force depends on the average pressure which is effectively h/2.
- Therefore, the ratio simplifies to:
Ratio = Total thrust on bottom / Total thrust on sides = (ρgh × Area) / (1/2 × ρg(h/2) × Height of side) = 1.
Why Use h/2 for Center Pressure?
- The center of pressure is always considered at h/2 for the vertical sides because it represents the average force exerted across the surface.
- The additional consideration of MOI does not apply here because we are focusing on the average effect of pressure across the height of the tank.
In conclusion, the average pressure at h/2 provides a straightforward calculation for thrust forces in fluid mechanics. Thus, the ratio remains consistent at 1, confirming the balance of forces in the system.
To analyze the thrust force on the bottom of the tank and on its sides, we need to consider the principles of fluid mechanics.
Thrust Force on the Bottom of the Tank
- The total thrust force on the bottom is calculated using the formula:
Thrust Force = Pressure × Area
- The pressure at the bottom of the tank is determined by the height of the water column (h). Since the tank is full, the pressure at the bottom is given by:
Pressure = ρgh (where ρ is the density of water and g is the acceleration due to gravity).
Thrust Force on the Sides of the Tank
- The thrust force on the vertical sides of the tank varies with depth due to hydrostatic pressure.
- The average pressure on a side is considered to calculate the total thrust force. The average height of the center of pressure is located at h/2 from the top, not accounting for the moment of inertia (MOI) since the average pressure gives us a simplified view.
Ratio of Forces
- The ratio of the total thrust force on the bottom of the tank to that on any side is derived as follows:
- Bottom thrust force is proportional to h.
- Side thrust force depends on the average pressure which is effectively h/2.
- Therefore, the ratio simplifies to:
Ratio = Total thrust on bottom / Total thrust on sides = (ρgh × Area) / (1/2 × ρg(h/2) × Height of side) = 1.
Why Use h/2 for Center Pressure?
- The center of pressure is always considered at h/2 for the vertical sides because it represents the average force exerted across the surface.
- The additional consideration of MOI does not apply here because we are focusing on the average effect of pressure across the height of the tank.
In conclusion, the average pressure at h/2 provides a straightforward calculation for thrust forces in fluid mechanics. Thus, the ratio remains consistent at 1, confirming the balance of forces in the system.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
Question: A house-top water tank is made of flat plates and is full to the brim. Its height is twice that of any side. The ratio of total thrust force on the bottom of the tank to that on any side will be:Doubt:on everywhere it's answer is showing 1. while calculating the vertical side they have considered average by assuming uniform pressure which is not mentioned in Question. Kindly help with it. Why are we taking height of centre pressure as h/2, why not {h/2+ MOI/A. h/2}.?
Question Description
Question: A house-top water tank is made of flat plates and is full to the brim. Its height is twice that of any side. The ratio of total thrust force on the bottom of the tank to that on any side will be:Doubt:on everywhere it's answer is showing 1. while calculating the vertical side they have considered average by assuming uniform pressure which is not mentioned in Question. Kindly help with it. Why are we taking height of centre pressure as h/2, why not {h/2+ MOI/A. h/2}.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Question: A house-top water tank is made of flat plates and is full to the brim. Its height is twice that of any side. The ratio of total thrust force on the bottom of the tank to that on any side will be:Doubt:on everywhere it's answer is showing 1. while calculating the vertical side they have considered average by assuming uniform pressure which is not mentioned in Question. Kindly help with it. Why are we taking height of centre pressure as h/2, why not {h/2+ MOI/A. h/2}.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Question: A house-top water tank is made of flat plates and is full to the brim. Its height is twice that of any side. The ratio of total thrust force on the bottom of the tank to that on any side will be:Doubt:on everywhere it's answer is showing 1. while calculating the vertical side they have considered average by assuming uniform pressure which is not mentioned in Question. Kindly help with it. Why are we taking height of centre pressure as h/2, why not {h/2+ MOI/A. h/2}.?.
Question: A house-top water tank is made of flat plates and is full to the brim. Its height is twice that of any side. The ratio of total thrust force on the bottom of the tank to that on any side will be:Doubt:on everywhere it's answer is showing 1. while calculating the vertical side they have considered average by assuming uniform pressure which is not mentioned in Question. Kindly help with it. Why are we taking height of centre pressure as h/2, why not {h/2+ MOI/A. h/2}.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Question: A house-top water tank is made of flat plates and is full to the brim. Its height is twice that of any side. The ratio of total thrust force on the bottom of the tank to that on any side will be:Doubt:on everywhere it's answer is showing 1. while calculating the vertical side they have considered average by assuming uniform pressure which is not mentioned in Question. Kindly help with it. Why are we taking height of centre pressure as h/2, why not {h/2+ MOI/A. h/2}.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Question: A house-top water tank is made of flat plates and is full to the brim. Its height is twice that of any side. The ratio of total thrust force on the bottom of the tank to that on any side will be:Doubt:on everywhere it's answer is showing 1. while calculating the vertical side they have considered average by assuming uniform pressure which is not mentioned in Question. Kindly help with it. Why are we taking height of centre pressure as h/2, why not {h/2+ MOI/A. h/2}.?.
Solutions for Question: A house-top water tank is made of flat plates and is full to the brim. Its height is twice that of any side. The ratio of total thrust force on the bottom of the tank to that on any side will be:Doubt:on everywhere it's answer is showing 1. while calculating the vertical side they have considered average by assuming uniform pressure which is not mentioned in Question. Kindly help with it. Why are we taking height of centre pressure as h/2, why not {h/2+ MOI/A. h/2}.? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of Question: A house-top water tank is made of flat plates and is full to the brim. Its height is twice that of any side. The ratio of total thrust force on the bottom of the tank to that on any side will be:Doubt:on everywhere it's answer is showing 1. while calculating the vertical side they have considered average by assuming uniform pressure which is not mentioned in Question. Kindly help with it. Why are we taking height of centre pressure as h/2, why not {h/2+ MOI/A. h/2}.? defined & explained in the simplest way possible. Besides giving the explanation of
Question: A house-top water tank is made of flat plates and is full to the brim. Its height is twice that of any side. The ratio of total thrust force on the bottom of the tank to that on any side will be:Doubt:on everywhere it's answer is showing 1. while calculating the vertical side they have considered average by assuming uniform pressure which is not mentioned in Question. Kindly help with it. Why are we taking height of centre pressure as h/2, why not {h/2+ MOI/A. h/2}.?, a detailed solution for Question: A house-top water tank is made of flat plates and is full to the brim. Its height is twice that of any side. The ratio of total thrust force on the bottom of the tank to that on any side will be:Doubt:on everywhere it's answer is showing 1. while calculating the vertical side they have considered average by assuming uniform pressure which is not mentioned in Question. Kindly help with it. Why are we taking height of centre pressure as h/2, why not {h/2+ MOI/A. h/2}.? has been provided alongside types of Question: A house-top water tank is made of flat plates and is full to the brim. Its height is twice that of any side. The ratio of total thrust force on the bottom of the tank to that on any side will be:Doubt:on everywhere it's answer is showing 1. while calculating the vertical side they have considered average by assuming uniform pressure which is not mentioned in Question. Kindly help with it. Why are we taking height of centre pressure as h/2, why not {h/2+ MOI/A. h/2}.? theory, EduRev gives you an
ample number of questions to practice Question: A house-top water tank is made of flat plates and is full to the brim. Its height is twice that of any side. The ratio of total thrust force on the bottom of the tank to that on any side will be:Doubt:on everywhere it's answer is showing 1. while calculating the vertical side they have considered average by assuming uniform pressure which is not mentioned in Question. Kindly help with it. Why are we taking height of centre pressure as h/2, why not {h/2+ MOI/A. h/2}.? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup