Answer:
The flow rate of oil through the pipe is 1.513E-7 m³/s.
Explanation:
Given
Density, ρ = 850 kg/m³
Kinematic viscosity, v = 0.00062 m²/s
Diameter, d = 8-mm = 0.008m
Length of horizontal pipe, L = 42-m
Height, h = 4-m.
We'll solve the flow rate of oil through the pipe by using Hagen-Poiseuille equation.
This is given as
∆P = (128μLQ)/πD⁴
Where ∆P = Rate of change of pressure
μ = Dynamic Viscosity
Q = Flow rate of oil through the pipe.
First, we need to determine the dynamic viscosity and the rate of change in pressure
Dynamic Viscosity, μ = Density (ρ) * Kinematic viscosity (v)
μ = 850 kg/m³ * 0.00062 m²/s
μ = 0.527kg/ms
Then, we calculate the rate of change of pressure.
Assuming that the velocity through the pipe is so small;
∆P = Pressure at the bottom of the tank
∆P = Density (ρ) * Acceleration of gravity (g) * Height (h)
Taking g = 9.8m/s²
∆P = 850kg/m³ x 9.8m/s² x 4m
∆P = 33320N/m²
Recall that Hagen-Poiseuille equation.
∆P = (128μLQ)/πD⁴ --- Make Q the subject of formula
Q = (πD⁴P)/(128μL)
By substituton;
Q = (π * 0.008⁴ * 33320)/(128 * 0.527 * 42)
Q = 0.00000015133693643099
Q = 1.513E-7 m³/s.
Hence, the flow rate of oil through the pipe is 1.513E-7 m³/s.
