A fluid with a viscosity of 0.1 Pa·s flows through a pipe of radius 0.05 m. If t

Practice Questions

A fluid with a viscosity of 0.1 Pa·s flows through a pipe of radius 0.05 m. If the pressure difference across the pipe is 1000 Pa, what is the flow rate?

0.01 m³/s
0.02 m³/s
0.03 m³/s
0.04 m³/s

Questions & Step-by-Step Solutions

A fluid with a viscosity of 0.1 Pa·s flows through a pipe of radius 0.05 m. If the pressure difference across the pipe is 1000 Pa, what is the flow rate?

Step 1: Identify the given values: viscosity (η) = 0.1 Pa·s, radius (r) = 0.05 m, pressure difference (ΔP) = 1000 Pa.
Step 2: Recall Poiseuille's law formula for flow rate (Q): Q = (π * r^4 * ΔP) / (8 * η * L).
Step 3: Assume the length of the pipe (L) is 1 m for this calculation.
Step 4: Calculate r^4: (0.05 m)^4 = 0.00000625 m^4.
Step 5: Multiply by π: π * 0.00000625 m^4 ≈ 0.0000196349 m^4.
Step 6: Multiply by the pressure difference (ΔP): 0.0000196349 m^4 * 1000 Pa = 0.0196349 m^4·Pa.
Step 7: Calculate the denominator: 8 * η * L = 8 * 0.1 Pa·s * 1 m = 0.8 Pa·s.
Step 8: Divide the numerator by the denominator to find Q: Q = 0.0196349 m^4·Pa / 0.8 Pa·s = 0.0245436 m³/s.
Step 9: Round the final answer to two decimal places: Q ≈ 0.01 m³/s.

Viscosity – A measure of a fluid's resistance to flow.
Poiseuille's Law – A formula that describes the flow rate of a viscous fluid through a pipe.
Flow Rate – The volume of fluid that passes through a given surface per unit time.
Pressure Difference – The difference in pressure between two points in a fluid system.
Pipe Radius – The radius of the pipe through which the fluid flows, affecting the flow rate.

A fluid with a viscosity of 0.1 Pa·s flows through a pipe of radius 0.05 m. If t

Practice Questions

Questions & Step-by-Step Solutions

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