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In a liquid flowing through a pipe, the pressure difference between its ends is made half and radius is doubled. If the initial rate of flow of liquid was Q, then new rate of flow of liquid through the pipe is
- a)32 Q
- b)8 Q
- c)Q
- d)0.25 Q
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
In a liquid flowing through a pipe, the pressure difference between it...
Explanation:
Given,
- Pressure difference between the ends of the pipe is made half.
- Radius of the pipe is doubled.
- Initial rate of flow of liquid through the pipe is Q.
We need to find the new rate of flow of liquid through the pipe.
Formula:
The rate of flow of liquid through a pipe is given by the formula:
Q = (πr^4ΔP) / (8ηl)
where,
- Q is the rate of flow of liquid through the pipe.
- r is the radius of the pipe.
- ΔP is the pressure difference between the ends of the pipe.
- η is the viscosity of the liquid.
- l is the length of the pipe.
Calculation:
Let the new radius of the pipe be r'. According to the problem statement,
- Pressure difference is made half. Hence, ΔP' = ΔP/2.
- Radius is doubled. Hence, r' = 2r.
Substituting these values in the formula for rate of flow of liquid through the pipe, we get:
Q' = (πr'^4ΔP') / (8ηl)
Q' = (π(2r)^4(ΔP/2)) / (8ηl)
Q' = 16(πr^4ΔP) / (8ηl)
Q' = 2Q
Hence, the new rate of flow of liquid through the pipe is 2Q.
Answer:
Option (B) 8Q is the correct answer.
Given,
- Pressure difference between the ends of the pipe is made half.
- Radius of the pipe is doubled.
- Initial rate of flow of liquid through the pipe is Q.
We need to find the new rate of flow of liquid through the pipe.
Formula:
The rate of flow of liquid through a pipe is given by the formula:
Q = (πr^4ΔP) / (8ηl)
where,
- Q is the rate of flow of liquid through the pipe.
- r is the radius of the pipe.
- ΔP is the pressure difference between the ends of the pipe.
- η is the viscosity of the liquid.
- l is the length of the pipe.
Calculation:
Let the new radius of the pipe be r'. According to the problem statement,
- Pressure difference is made half. Hence, ΔP' = ΔP/2.
- Radius is doubled. Hence, r' = 2r.
Substituting these values in the formula for rate of flow of liquid through the pipe, we get:
Q' = (πr'^4ΔP') / (8ηl)
Q' = (π(2r)^4(ΔP/2)) / (8ηl)
Q' = 16(πr^4ΔP) / (8ηl)
Q' = 2Q
Hence, the new rate of flow of liquid through the pipe is 2Q.
Answer:
Option (B) 8Q is the correct answer.
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Community Answer
In a liquid flowing through a pipe, the pressure difference between it...
Use Poiseuille's equation : (pi)P(radii to the power 4)/L8(Coefficient of viscosity)
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In a liquid flowing through a pipe, the pressure difference between its ends is made half and radius is doubled. If the initial rate of flow of liquid was Q, then new rate of flow of liquid through the pipe isa)32 Qb)8 Qc)Qd)0.25 QCorrect answer is option 'B'. Can you explain this answer?
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In a liquid flowing through a pipe, the pressure difference between its ends is made half and radius is doubled. If the initial rate of flow of liquid was Q, then new rate of flow of liquid through the pipe isa)32 Qb)8 Qc)Qd)0.25 QCorrect answer is option 'B'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about In a liquid flowing through a pipe, the pressure difference between its ends is made half and radius is doubled. If the initial rate of flow of liquid was Q, then new rate of flow of liquid through the pipe isa)32 Qb)8 Qc)Qd)0.25 QCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a liquid flowing through a pipe, the pressure difference between its ends is made half and radius is doubled. If the initial rate of flow of liquid was Q, then new rate of flow of liquid through the pipe isa)32 Qb)8 Qc)Qd)0.25 QCorrect answer is option 'B'. Can you explain this answer?.
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