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A capillary tube is 30 mm long and 1 mm bore. The heat required to produce a flow rate of 8 mm3/s is 30 mm. The fluid density is 800 kg/m3. Calculate the dynamic viscosity of the oil.
- a)20.1 cP
- b)24.1 cP
- c)20.0 cP
- d)24.0 cP
Correct answer is option 'B'. Can you explain this answer?
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A capillary tube is 30 mm long and 1 mm bore. The heat required to pr...
Rearranging Poiseuille’s equation we get
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A capillary tube is 30 mm long and 1 mm bore. The heat required to pr...
To solve this problem, we can use the Hagen-Poiseuille equation, which relates the flow rate through a capillary tube to the pressure difference and the properties of the fluid and the tube.
The Hagen-Poiseuille equation is given by:
Q = (π * r^4 * ΔP) / (8 * μ * L)
where:
Q = flow rate
r = radius of the capillary tube
ΔP = pressure difference across the tube
μ = dynamic viscosity of the fluid
L = length of the tube
Given:
Length of the tube (L) = 30 mm = 0.03 m
Radius of the tube (r) = 1 mm / 2 = 0.001 m
Flow rate (Q) = 8 mm^3/s = 8 * 10^-9 m^3/s
We need to find the dynamic viscosity (μ).
To find the pressure difference (ΔP), we can use the equation:
ΔP = (Q * 8 * μ * L) / (π * r^4)
Now, let's substitute the given values into the equation to find the pressure difference:
ΔP = (8 * 10^-9 * 8 * μ * 0.03) / (π * (0.001)^4)
Simplifying the equation:
ΔP = (1.92 * 10^-7 * μ) / (π * 10^-12)
To find the value of ΔP, we can use the given information that the heat required to produce the flow rate of 8 mm^3/s is 30 mm. The heat (Q) is directly proportional to the pressure difference (ΔP). Therefore, we can write:
30 mm = ΔP
Converting 30 mm to Pascal (Pa):
30 mm = 30 * 9.81 Pa = 294.3 Pa
Now, let's equate the two expressions for ΔP and solve for μ:
294.3 Pa = (1.92 * 10^-7 * μ) / (π * 10^-12)
Simplifying the equation:
μ = (294.3 * π * 10^-12) / (1.92 * 10^-7)
μ ≈ 24.1 cP
Therefore, the correct answer is option B: 24.1 cP.
The Hagen-Poiseuille equation is given by:
Q = (π * r^4 * ΔP) / (8 * μ * L)
where:
Q = flow rate
r = radius of the capillary tube
ΔP = pressure difference across the tube
μ = dynamic viscosity of the fluid
L = length of the tube
Given:
Length of the tube (L) = 30 mm = 0.03 m
Radius of the tube (r) = 1 mm / 2 = 0.001 m
Flow rate (Q) = 8 mm^3/s = 8 * 10^-9 m^3/s
We need to find the dynamic viscosity (μ).
To find the pressure difference (ΔP), we can use the equation:
ΔP = (Q * 8 * μ * L) / (π * r^4)
Now, let's substitute the given values into the equation to find the pressure difference:
ΔP = (8 * 10^-9 * 8 * μ * 0.03) / (π * (0.001)^4)
Simplifying the equation:
ΔP = (1.92 * 10^-7 * μ) / (π * 10^-12)
To find the value of ΔP, we can use the given information that the heat required to produce the flow rate of 8 mm^3/s is 30 mm. The heat (Q) is directly proportional to the pressure difference (ΔP). Therefore, we can write:
30 mm = ΔP
Converting 30 mm to Pascal (Pa):
30 mm = 30 * 9.81 Pa = 294.3 Pa
Now, let's equate the two expressions for ΔP and solve for μ:
294.3 Pa = (1.92 * 10^-7 * μ) / (π * 10^-12)
Simplifying the equation:
μ = (294.3 * π * 10^-12) / (1.92 * 10^-7)
μ ≈ 24.1 cP
Therefore, the correct answer is option B: 24.1 cP.
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Question Description
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A capillary tube is 30 mm long and 1 mm bore. The heat required to produce a flow rate of 8 mm3/s is 30 mm. The fluid density is 800 kg/m3. Calculate the dynamic viscosity of the oil.a)20.1 cPb)24.1 cPc)20.0 cPd)24.0 cPCorrect answer is option 'B'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A capillary tube is 30 mm long and 1 mm bore. The heat required to produce a flow rate of 8 mm3/s is 30 mm. The fluid density is 800 kg/m3. Calculate the dynamic viscosity of the oil.a)20.1 cPb)24.1 cPc)20.0 cPd)24.0 cPCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A capillary tube is 30 mm long and 1 mm bore. The heat required to produce a flow rate of 8 mm3/s is 30 mm. The fluid density is 800 kg/m3. Calculate the dynamic viscosity of the oil.a)20.1 cPb)24.1 cPc)20.0 cPd)24.0 cPCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A capillary tube is 30 mm long and 1 mm bore. The heat required to produce a flow rate of 8 mm3/s is 30 mm. The fluid density is 800 kg/m3. Calculate the dynamic viscosity of the oil.a)20.1 cPb)24.1 cPc)20.0 cPd)24.0 cPCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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