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The rate of steady volume flow of water through a capillary tube of length / and radius 'r' under a pressure difference of P is V. This tube is connected with another tube of the same length but half the radius in series. Then the rate of steady volume flow through them is (The pressure difference across the combination is P)
- a)V/16
- b)V/17
- c)16V/17
- d)17V/16
Correct answer is option 'B'. Can you explain this answer?
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The rate of steady volume flow of water through a capillary tube of le...
Given Data:
- Length of capillary tube: l
- Radius of capillary tube: r
- Pressure difference across the tube: P
- Rate of steady volume flow through a single capillary tube: V
Calculation:
- The rate of flow of a liquid through a capillary tube is given by Poiseuille's law: V = πr^4(P)/(8ηl), where η is the viscosity of the liquid.
- For the first capillary tube, the rate of flow is V.
- For the second capillary tube (half the radius of the first), the rate of flow will be V' = π(r/2)^4(P)/(8ηl) = V/16.
- When connected in series, the total rate of flow through the combination is the sum of the rates of flow through each tube: V_total = V + V/16 = 17V/16.
Therefore, the correct answer is option B: V/17.
- Length of capillary tube: l
- Radius of capillary tube: r
- Pressure difference across the tube: P
- Rate of steady volume flow through a single capillary tube: V
Calculation:
- The rate of flow of a liquid through a capillary tube is given by Poiseuille's law: V = πr^4(P)/(8ηl), where η is the viscosity of the liquid.
- For the first capillary tube, the rate of flow is V.
- For the second capillary tube (half the radius of the first), the rate of flow will be V' = π(r/2)^4(P)/(8ηl) = V/16.
- When connected in series, the total rate of flow through the combination is the sum of the rates of flow through each tube: V_total = V + V/16 = 17V/16.
Therefore, the correct answer is option B: V/17.
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Community Answer
The rate of steady volume flow of water through a capillary tube of le...
Rate of flow of liquid V = P/R
where liquid resistance
For another tube liquid resistance
For the series combination
where liquid resistance
For another tube liquid resistance
For the series combination
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The rate of steady volume flow of water through a capillary tube of length / and radius r under a pressure difference of P is V. This tube is connected with another tube of the same length but half the radius in series. Then the rate of steady volume flow through them is (The pressure difference across the combination is P)a)V/16b)V/17c)16V/17d)17V/16Correct answer is option 'B'. Can you explain this answer?
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