The Darcy-Weisbach equation is expressed as
- Ahf = f (L/D) (V²/2g)Correct
- Bhf = (L/D) (fV²/2g)
- Chf = f (2gL/D)
- Dhf = 2g/(fLD)
Solution
Concept
Darcy-Weisbach Equation
Formula
hf = f × (L / D) × (V² / 2g)
Step-by-step solution
1. Identify the given values for friction factor (f), pipe length (L), pipe diameter (D), flow velocity (V), and gravitational acceleration (g). 2. Calculate the length-to-diameter ratio (L / D) and velocity head (V² / 2g). 3. Multiply the friction factor by the length-to-diameter ratio and velocity head to find head loss (hf).
Explanation
The Darcy-Weisbach equation calculates head loss due to friction in a pipe. It states that head loss (hf) is equal to the friction factor (f) multiplied by the ratio of pipe length to diameter (L/D) and the velocity head (V²/2g).
Shortcut
Remember the phrase: "Friction Factor times Length over Diameter, with Velocity squared over 2g" or the formula components: f (friction), L/D (length/diameter ratio), and V²/2g (velocity head).
Common mistake
Students often confuse the Darcy friction factor (f) with the Fanning friction coefficient (f'), which leads to choosing incorrect numerical values or misinterpreting the position of terms like 2g or velocity head in the formula.
Correct answer: A) hf = f (L/D) (V²/2g)