Question
Glycerine flows steadily through a horizontal tube of length 1.5 m and radius 1.0 cm. If the amount of glycerine collected per second at one end is 4.0 × 10–3 kg s–1, what is the pressure difference between the two ends of the tube? (Density of glycerine = 1.3 × 103 kg m–3 and viscosity of glycerine = 0.83 Pa s). [You may also like to check if the assumption of laminar flow in the tube is correct].
Solution
Length of the horizontal tube, l = 1.5 m
Radius of the tube, r = 1 cm = 0.01 m
Diameter of the tube, d = 2r = 0.02 m
Glycerine is flowing at a rate of 4.0 × 10–3 kg s–1.
Mass of the substance, M = 4.0 × 10–3 kg s–1
Density of glycerine, ρ = 1.3 × 103 kg m–3
Viscosity of glycerine, η = 0.83 Pa s
Volume of glycerine flowing per sec,
V =
According to Poiseville’s formula, we have the relation for the rate of flow,
Radius of the tube, r = 1 cm = 0.01 m
Diameter of the tube, d = 2r = 0.02 m
Glycerine is flowing at a rate of 4.0 × 10–3 kg s–1.
Mass of the substance, M = 4.0 × 10–3 kg s–1
Density of glycerine, ρ = 1.3 × 103 kg m–3
Viscosity of glycerine, η = 0.83 Pa s
Volume of glycerine flowing per sec,
V =
According to Poiseville’s formula, we have the relation for the rate of flow,
