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For a circular pipe with diameter D and having laminar flow, the head loss due to friction is ________.
- a)directly proportional to D4
- b)inversely proportional to D4
- c)directly proportional to D2
- d)inversely proportional to D2
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
For a circular pipe with diameter D and having laminar flow, the head ...
Head loss due to friction in a circular pipe with laminar flow is inversely proportional to the fourth power of the diameter (D) of the pipe. This relationship is known as the Darcy-Weisbach equation.
Explanation:
The Darcy-Weisbach equation is commonly used to calculate the head loss due to friction in a pipe. It is given by the following equation:
hL = f (L/D) (V^2 / 2g)
where:
hL is the head loss due to friction,
f is the Darcy friction factor,
L is the length of the pipe,
D is the diameter of the pipe,
V is the velocity of the fluid,
g is the acceleration due to gravity.
To determine the relationship between head loss and diameter, we can rearrange the equation as follows:
hL = f (L/D) (V^2 / 2g)
hL = (fL/2g) * (V^2 / D)
From this equation, we can see that the head loss is directly proportional to (fL/2g) and (V^2 / D). Now, let's consider these terms separately.
1. (fL/2g)
The term (fL/2g) is known as the friction factor, which is a dimensionless quantity that depends on the roughness of the pipe surface and the Reynolds number. It is independent of the diameter of the pipe.
2. (V^2 / D)
The term (V^2 / D) represents the velocity head, which is the kinetic energy per unit weight of the fluid. This term is directly proportional to the square of the velocity and inversely proportional to the diameter.
Combining these two terms, we can conclude that the head loss due to friction is inversely proportional to the diameter (D) of the pipe. Therefore, the correct answer is option B - inversely proportional to D^4.
The relationship between head loss and diameter is important in the design and analysis of piping systems. It helps engineers determine the appropriate pipe diameter for a given flow rate and pressure drop.
Explanation:
The Darcy-Weisbach equation is commonly used to calculate the head loss due to friction in a pipe. It is given by the following equation:
hL = f (L/D) (V^2 / 2g)
where:
hL is the head loss due to friction,
f is the Darcy friction factor,
L is the length of the pipe,
D is the diameter of the pipe,
V is the velocity of the fluid,
g is the acceleration due to gravity.
To determine the relationship between head loss and diameter, we can rearrange the equation as follows:
hL = f (L/D) (V^2 / 2g)
hL = (fL/2g) * (V^2 / D)
From this equation, we can see that the head loss is directly proportional to (fL/2g) and (V^2 / D). Now, let's consider these terms separately.
1. (fL/2g)
The term (fL/2g) is known as the friction factor, which is a dimensionless quantity that depends on the roughness of the pipe surface and the Reynolds number. It is independent of the diameter of the pipe.
2. (V^2 / D)
The term (V^2 / D) represents the velocity head, which is the kinetic energy per unit weight of the fluid. This term is directly proportional to the square of the velocity and inversely proportional to the diameter.
Combining these two terms, we can conclude that the head loss due to friction is inversely proportional to the diameter (D) of the pipe. Therefore, the correct answer is option B - inversely proportional to D^4.
The relationship between head loss and diameter is important in the design and analysis of piping systems. It helps engineers determine the appropriate pipe diameter for a given flow rate and pressure drop.
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Community Answer
For a circular pipe with diameter D and having laminar flow, the head ...
Laminar flow through a circular pipe:
In a constant diameter pipe, the pressure drops uniformly along the pipe length (except for the entrance region)
∵ we know that the average velocity through a circular pipe;
Now, ΔP = ρ g Hl
Putting ΔP, from the above equation, we get
Hl ∝ 1 / D4
From the above expression, it is clear that hydraulic gradient is inversely proportional to D4
In a constant diameter pipe, the pressure drops uniformly along the pipe length (except for the entrance region)
∵ we know that the average velocity through a circular pipe;
Now, ΔP = ρ g Hl
Putting ΔP, from the above equation, we get
Hl ∝ 1 / D4
From the above expression, it is clear that hydraulic gradient is inversely proportional to D4
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For a circular pipe with diameter D and having laminar flow, the head loss due to friction is ________.a)directly proportional to D4b)inversely proportional to D4c)directly proportional to D2d)inversely proportional to D2Correct answer is option 'B'. Can you explain this answer?
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