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The frictional resistance for fluids in motion is
- a)proportional to the velocity in laminar flow and to the square of the velocity in turbulent flow
- b)proportional to the square of the velocity in laminar flow and to the velocity in turbulent flow
- c)proportional to the velocity in both laminar flow and turbulent flow
- d)proportional to the square of the velocity in both laminar flow and turbulent flow
Correct answer is option 'A'. Can you explain this answer?
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The frictional resistance for fluids in motion isa)proportional to the...
Explanation: According to the laws of fluid friction, rf / v (for steady streamline flow) and rf / v2(for turbulent flow), where rf is the frictional resistance and v is the velocity of flow.
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The frictional resistance for fluids in motion isa)proportional to the...
Frictional Resistance for Fluids in Motion
Frictional resistance refers to the force that opposes motion between two surfaces in contact. In fluid mechanics, frictional resistance is the force that opposes the motion of a fluid as it flows over a surface. The frictional resistance for fluids in motion can be expressed mathematically using the Darcy-Weisbach equation:
f = (ΔP/2gL) * (D/H)^5.02
where:
f = friction factor
ΔP = pressure drop
g = acceleration due to gravity
L = length of the pipe
D = diameter of the pipe
H = head loss
Proportional to Velocity
The frictional resistance for fluids in motion is proportional to the velocity of the fluid. However, the proportionality constant depends on whether the flow is laminar or turbulent.
Laminar Flow
In laminar flow, the frictional resistance is proportional to the velocity of the fluid. This means that if the velocity of the fluid doubles, the frictional resistance also doubles. Mathematically, this can be expressed as:
f ∝ v
where:
f = frictional resistance
v = velocity of the fluid
Turbulent Flow
In turbulent flow, the frictional resistance is proportional to the square of the velocity of the fluid. This means that if the velocity of the fluid doubles, the frictional resistance quadruples. Mathematically, this can be expressed as:
f ∝ v^2
where:
f = frictional resistance
v = velocity of the fluid
Conclusion
In conclusion, the correct answer is option A. The frictional resistance for fluids in motion is proportional to the velocity in laminar flow and to the square of the velocity in turbulent flow.
Frictional resistance refers to the force that opposes motion between two surfaces in contact. In fluid mechanics, frictional resistance is the force that opposes the motion of a fluid as it flows over a surface. The frictional resistance for fluids in motion can be expressed mathematically using the Darcy-Weisbach equation:
f = (ΔP/2gL) * (D/H)^5.02
where:
f = friction factor
ΔP = pressure drop
g = acceleration due to gravity
L = length of the pipe
D = diameter of the pipe
H = head loss
Proportional to Velocity
The frictional resistance for fluids in motion is proportional to the velocity of the fluid. However, the proportionality constant depends on whether the flow is laminar or turbulent.
Laminar Flow
In laminar flow, the frictional resistance is proportional to the velocity of the fluid. This means that if the velocity of the fluid doubles, the frictional resistance also doubles. Mathematically, this can be expressed as:
f ∝ v
where:
f = frictional resistance
v = velocity of the fluid
Turbulent Flow
In turbulent flow, the frictional resistance is proportional to the square of the velocity of the fluid. This means that if the velocity of the fluid doubles, the frictional resistance quadruples. Mathematically, this can be expressed as:
f ∝ v^2
where:
f = frictional resistance
v = velocity of the fluid
Conclusion
In conclusion, the correct answer is option A. The frictional resistance for fluids in motion is proportional to the velocity in laminar flow and to the square of the velocity in turbulent flow.
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The frictional resistance for fluids in motion isa)proportional to the velocity in laminar flow and to the square of the velocity in turbulent flowb)proportional to the square of the velocity in laminar flow and to the velocity in turbulent flowc)proportional to the velocity in both laminar flow and turbulent flowd)proportional to the square of the velocity in both laminar flow and turbulent flowCorrect answer is option 'A'. Can you explain this answer?
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