A pressure difference of 6.00 x 104 Pa is required to maintain a volume flow rate of 0.400 m3 /s for a viscous fluid flowing thr
ough a section of cylindrical pipe that has a radius 0.330 m. What pressure difference is required to maintain the same volume flow rate if the radius of the pipe is decreased to 0.110 m?
To determine how variables affect the flow rate of an incompressible fluid undergoing laminate flow in a cylindrical tube, we use Poiseuille's equation.
Q = Πr⁴ / 8η * [(p₁ - p₂) / L]
Q = 0.40 m³/s
P₁ - P₂ = 6*10⁴ pa
r₁ = 0.33m
r₂ = 0.11m
According to Poiseuille's law, the pressure difference is inversely proportional to the radius of the pipe raised to power of 4.
