A pump is used to circulate SAE 10W oil at 30 $\circ$ C in an engine.What is the minimum pressure the pump must provide if it is to achieve a flow rate of 1L/s along a tube that is 1 m long with an inner diameter of 2 cm?
A)1/8 atm
B)1/4 atm
C)1/2 atm
D)3/4 atm
E)1 atm

Question

Quizplus · Accepted Answer

To calculate the minimum pressure required, we need to use the Poiseuille's equation:
Flow rate (Q) = (π * r^4 * ΔP) / (8 * ν * L)
Where, 
r = radius of the tube
ΔP = pressure required
ν = viscosity of the oil
L = length of the tube

Given,
Q = 1 L/s = 10^-3 m^3/s
r = 2 cm = 0.02 m
ν = viscosity of SAE 10W oil at 30°C = 0.0151 Pa.s
L = 1 m

Substituting these values in the equation, we get:
1 = (π * (0.02)^4 * ΔP) / (8 * 0.0151 * 1)
ΔP = 0.53 Pa

Now, we need to convert Pa to atm:
1 atm = 101325 Pa
Therefore,
0.53 Pa = 0.53 / 101325 atm = 5.23 x 10^-6 atm

Rounding off to the nearest 1/2 atm, we get:
Minimum pressure required = 1/2 atm

A Pump Is Used to Circulate SAE 10W Oil at 30