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?
Practice Questions
1 question
Q1
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
Using Poiseuille's law, the flow rate Q = (π * r^4 * ΔP) / (8 * η * L). Assuming L = 1 m, Q = (π * (0.05)^4 * 1000) / (8 * 0.1 * 1) = 0.01 m³/s.
Questions & Step-by-step Solutions
1 item
Q
Q: 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?
Solution: Using Poiseuille's law, the flow rate Q = (π * r^4 * ΔP) / (8 * η * L). Assuming L = 1 m, Q = (π * (0.05)^4 * 1000) / (8 * 0.1 * 1) = 0.01 m³/s.
Steps: 9
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.
