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Which of the following is the expression of the Carmen equation where symbols have their usual meanings? 
  • a)
    hf = f* (L/(s *d)) * ((1-e)/e3) * (v2/g)
  • b)
    hf = f* (L/(s *d)) * ((1-e)/e3) * (v/g)
  • c)
    hf = f* (L/(s *d)) * ((1-e)/e) * (v2/g)
  • d)
    hf = f* (L/(s *d)) * ((1-e)/e2) * (v2/g)
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Which of the following is the expression of the Carmen equation where ...
Explanation: The expression of the Carmen equation is given by hf = f* (L/(s *d)) * ((1-e) /e3) * (v2/g) where hf =head loss, d= diameter of pipe. L= length of pipe and v=approach velocity.
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Most Upvoted Answer
Which of the following is the expression of the Carmen equation where ...
The correct expression of the Carmen equation is option 'A': hf = f* (L/(s *d)) * ((1-e)/e3) * (v2/g).

Explanation:
The Carmen equation is used to calculate the pressure drop (head loss) in a fluid flow system. It is commonly used in chemical engineering and fluid mechanics.

In the equation, the symbols have the following meanings:
- hf: head loss or pressure drop (in units of length, such as meters)
- f*: Darcy friction factor (dimensionless)
- L: length of the pipe or flow path (in units of length, such as meters)
- s: hydraulic radius of the flow path (in units of length, such as meters)
- d: diameter of the pipe or flow path (in units of length, such as meters)
- e: roughness height or equivalent sand grain roughness (in units of length, such as meters)
- v: velocity of the fluid flow (in units of length per time, such as meters per second)
- g: acceleration due to gravity (in units of length per squared time, such as meters per second squared)

Now, let's break down the expression and understand each term:

1. f* (L/(s *d)):
- This term represents the frictional losses in the flow system.
- f* is the Darcy friction factor, which takes into account the pipe roughness and flow conditions.
- L is the length of the pipe or flow path.
- s is the hydraulic radius, which is a measure of flow area per unit wetted perimeter.
- d is the diameter of the pipe or flow path.

2. ((1-e)/e3):
- This term accounts for the roughness of the pipe or flow path.
- e is the roughness height or equivalent sand grain roughness.
- ((1-e)/e3) is a dimensionless term that adjusts the frictional losses based on the pipe roughness.

3. (v2/g):
- This term represents the kinetic energy head of the fluid flow.
- v is the velocity of the fluid flow.
- g is the acceleration due to gravity.
- (v2/g) is a dimensionless term that relates the fluid velocity to the gravitational acceleration.

By multiplying these three terms together, we obtain the expression for the head loss or pressure drop in the Carmen equation.

In summary, the correct expression of the Carmen equation is:
hf = f* (L/(s *d)) * ((1-e)/e3) * (v2/g)
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