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At the bottom of a uniform cylindrical vessel of 30 cm height a horizontal capillary tube of 2mm inner diameter and 10 cm length is connected to discharge the liquid. Calculate the rate of discharge of the liquid if the vessel contains water of viscosity 0.01 poise to its 2/3 capacity. Take the density of water as 1 gm/cc.
- a)7.59 cm3/s
- b)6.59 cm3/s
- c)7.69 cm3/s
- d)6.69 cm3/s
Correct answer is option 'C'. Can you explain this answer?
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To calculate the rate of discharge of the liquid, we can use the Poiseuille's law, which states that the flow rate through a capillary tube is directly proportional to the pressure difference and the fourth power of the radius of the tube and inversely proportional to the viscosity of the liquid and the length of the tube.
Given:
Height of the cylindrical vessel (h) = 30 cm
Inner diameter of the capillary tube (d) = 2 mm = 0.2 cm
Length of the capillary tube (L) = 10 cm
Viscosity of water (η) = 0.01 poise
Density of water (ρ) = 1 gm/cc
Let's calculate the radius of the capillary tube:
Radius (r) = d/2 = 0.2 cm / 2 = 0.1 cm
Now, let's calculate the pressure difference:
The pressure difference can be calculated using the hydrostatic pressure formula:
Pressure difference (ΔP) = ρgh
Here, g is the acceleration due to gravity, which is approximately 9.8 m/s^2.
The height of the water column is given as 2/3 of the capacity of the vessel, which is 2/3 * 30 cm = 20 cm.
ΔP = 1 gm/cc * 9.8 m/s^2 * 20 cm * (1 m / 100 cm)
= 1 gm/cc * 9.8 m/s^2 * 0.2 m
= 1.96 gm/m^2
Now, let's calculate the rate of discharge:
Using Poiseuille's law, the rate of discharge (Q) is given by:
Q = (Π * r^4 * ΔP) / (8ηL)
Q = (Π * (0.1 cm)^4 * (1.96 gm/m^2)) / (8 * 0.01 poise * 10 cm)
= (Π * 0.0001 cm^4 * 1.96 gm/m^2) / (0.08 poise * 10 cm)
= (Π * 0.0001 cm^4 * 1.96 gm/m^2) / (0.8 gm/cm/s)
= (Π * 0.0001 * 1.96) / 0.8 cm^3/s
= 7.68 cm^3/s (approximately)
Therefore, the rate of discharge of the liquid is approximately 7.68 cm^3/s, which is closest to option C (7.69 cm^3/s).
Given:
Height of the cylindrical vessel (h) = 30 cm
Inner diameter of the capillary tube (d) = 2 mm = 0.2 cm
Length of the capillary tube (L) = 10 cm
Viscosity of water (η) = 0.01 poise
Density of water (ρ) = 1 gm/cc
Let's calculate the radius of the capillary tube:
Radius (r) = d/2 = 0.2 cm / 2 = 0.1 cm
Now, let's calculate the pressure difference:
The pressure difference can be calculated using the hydrostatic pressure formula:
Pressure difference (ΔP) = ρgh
Here, g is the acceleration due to gravity, which is approximately 9.8 m/s^2.
The height of the water column is given as 2/3 of the capacity of the vessel, which is 2/3 * 30 cm = 20 cm.
ΔP = 1 gm/cc * 9.8 m/s^2 * 20 cm * (1 m / 100 cm)
= 1 gm/cc * 9.8 m/s^2 * 0.2 m
= 1.96 gm/m^2
Now, let's calculate the rate of discharge:
Using Poiseuille's law, the rate of discharge (Q) is given by:
Q = (Π * r^4 * ΔP) / (8ηL)
Q = (Π * (0.1 cm)^4 * (1.96 gm/m^2)) / (8 * 0.01 poise * 10 cm)
= (Π * 0.0001 cm^4 * 1.96 gm/m^2) / (0.08 poise * 10 cm)
= (Π * 0.0001 cm^4 * 1.96 gm/m^2) / (0.8 gm/cm/s)
= (Π * 0.0001 * 1.96) / 0.8 cm^3/s
= 7.68 cm^3/s (approximately)
Therefore, the rate of discharge of the liquid is approximately 7.68 cm^3/s, which is closest to option C (7.69 cm^3/s).
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At the bottom of a uniform cylindrical vessel of 30 cm height a horizontal capillary tube of 2mm inner diameter and 10 cm length is connected to discharge the liquid. Calculate the rate of discharge of the liquid if the vessel contains water of viscosity 0.01 poise to its 2/3 capacity. Take the density of water as 1 gm/cc.a)7.59 cm3/sb)6.59 cm3/sc)7.69 cm3/sd)6.69 cm3/sCorrect answer is option 'C'. Can you explain this answer?
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At the bottom of a uniform cylindrical vessel of 30 cm height a horizontal capillary tube of 2mm inner diameter and 10 cm length is connected to discharge the liquid. Calculate the rate of discharge of the liquid if the vessel contains water of viscosity 0.01 poise to its 2/3 capacity. Take the density of water as 1 gm/cc.a)7.59 cm3/sb)6.59 cm3/sc)7.69 cm3/sd)6.69 cm3/sCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about At the bottom of a uniform cylindrical vessel of 30 cm height a horizontal capillary tube of 2mm inner diameter and 10 cm length is connected to discharge the liquid. Calculate the rate of discharge of the liquid if the vessel contains water of viscosity 0.01 poise to its 2/3 capacity. Take the density of water as 1 gm/cc.a)7.59 cm3/sb)6.59 cm3/sc)7.69 cm3/sd)6.69 cm3/sCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At the bottom of a uniform cylindrical vessel of 30 cm height a horizontal capillary tube of 2mm inner diameter and 10 cm length is connected to discharge the liquid. Calculate the rate of discharge of the liquid if the vessel contains water of viscosity 0.01 poise to its 2/3 capacity. Take the density of water as 1 gm/cc.a)7.59 cm3/sb)6.59 cm3/sc)7.69 cm3/sd)6.69 cm3/sCorrect answer is option 'C'. Can you explain this answer?.
At the bottom of a uniform cylindrical vessel of 30 cm height a horizontal capillary tube of 2mm inner diameter and 10 cm length is connected to discharge the liquid. Calculate the rate of discharge of the liquid if the vessel contains water of viscosity 0.01 poise to its 2/3 capacity. Take the density of water as 1 gm/cc.a)7.59 cm3/sb)6.59 cm3/sc)7.69 cm3/sd)6.69 cm3/sCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about At the bottom of a uniform cylindrical vessel of 30 cm height a horizontal capillary tube of 2mm inner diameter and 10 cm length is connected to discharge the liquid. Calculate the rate of discharge of the liquid if the vessel contains water of viscosity 0.01 poise to its 2/3 capacity. Take the density of water as 1 gm/cc.a)7.59 cm3/sb)6.59 cm3/sc)7.69 cm3/sd)6.69 cm3/sCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At the bottom of a uniform cylindrical vessel of 30 cm height a horizontal capillary tube of 2mm inner diameter and 10 cm length is connected to discharge the liquid. Calculate the rate of discharge of the liquid if the vessel contains water of viscosity 0.01 poise to its 2/3 capacity. Take the density of water as 1 gm/cc.a)7.59 cm3/sb)6.59 cm3/sc)7.69 cm3/sd)6.69 cm3/sCorrect answer is option 'C'. Can you explain this answer?.
Solutions for At the bottom of a uniform cylindrical vessel of 30 cm height a horizontal capillary tube of 2mm inner diameter and 10 cm length is connected to discharge the liquid. Calculate the rate of discharge of the liquid if the vessel contains water of viscosity 0.01 poise to its 2/3 capacity. Take the density of water as 1 gm/cc.a)7.59 cm3/sb)6.59 cm3/sc)7.69 cm3/sd)6.69 cm3/sCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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ample number of questions to practice At the bottom of a uniform cylindrical vessel of 30 cm height a horizontal capillary tube of 2mm inner diameter and 10 cm length is connected to discharge the liquid. Calculate the rate of discharge of the liquid if the vessel contains water of viscosity 0.01 poise to its 2/3 capacity. Take the density of water as 1 gm/cc.a)7.59 cm3/sb)6.59 cm3/sc)7.69 cm3/sd)6.69 cm3/sCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice GATE tests.
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