Which of the following represents Darcy’s friction factor in terms of...
Darcy Weisbach Equation for friction losses in circular pipe
where
L = length of the pipe,
D = diameter of the circular pipe,
V = mean velocity of the flow,
f = Darcy’s friction factor = 4 × F’,
F’ = coefficient of friction
hf = head loss due to friction
For Laminar Flow
Friction Factor
For Turbulent flow
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Which of the following represents Darcy’s friction factor in terms of...
Darcy’s friction factor is a dimensionless quantity used to characterize the fluid flow resistance in pipes. For laminar flow in circular pipes, the friction factor can be expressed in terms of the Reynolds number (Re) using the following equation:
f = 64/Re
Explanation:
Laminar flow refers to a smooth and orderly flow of fluid, where the fluid layers move parallel to each other. In circular pipes, laminar flow occurs at low flow rates or when the pipe diameter is relatively small.
The Reynolds number (Re) is a dimensionless quantity that represents the ratio of inertial forces to viscous forces in a flow. It is defined as:
Re = (ρVD)/μ
Where:
- ρ is the density of the fluid
- V is the velocity of the fluid
- D is the diameter of the pipe
- μ is the dynamic viscosity of the fluid
The friction factor (f) represents the resistance to flow due to internal friction between the fluid and the pipe walls. In laminar flow, the friction factor can be calculated using the following equation:
f = 16/Re
However, for the specific case of laminar flow in circular pipes, the friction factor is slightly different and can be expressed as:
f = 64/Re
This equation shows that as the Reynolds number decreases (indicating lower flow rates or smaller pipe diameters), the friction factor increases. This means that laminar flow in circular pipes experiences higher flow resistance compared to turbulent flow.
The correct answer to the question is option C, 64/Re, as it represents Darcy’s friction factor in terms of Reynolds number for laminar flow in circular pipes.