Question

If the flow rate through a tube, is originally 50 cm³/s, calculate the new flow rate(a) if the pressure difference, (AP), doubles; (b) if the viscosity of the fluid, n, doubles; (c) if the length of the tube, L, doubles; and (d) if the radius of the tube, r, doubles. Assume that in each case only the factor mentioned differs from the original conditions.

Answer 1

(a) If the pressure difference doubles, the flow rate can be calculated using the formula:
Q = (π * r^4 * ΔP) / (8 * η * L)
Let Q1 be the original flow rate and Q2 be the new flow rate.
Q2 = (π * r^4 * 2ΔP) / (8 * η * L)
Q2 = 2 * Q1
Q2 = 2 * 50 cm³/s
Q2 = 100 cm³/s
Therefore, the new flow rate if the pressure difference doubles is 100 cm³/s.
(b) If the viscosity of the fluid doubles, the flow rate can be calculated using the formula:
Q = (π * r^4 * ΔP) / (8 * 2η * L)
Q2 = (π * r^4 * ΔP) / (16 * η * L)
Q2 = Q1 / 2
Q2 = 50 cm³/s / 2
Q2 = 25 cm³/s
Therefore, the new flow rate if the viscosity of the fluid doubles is 25 cm³/s.
(c) If the length of the tube doubles, the flow rate can be calculated using the formula:
Q = (π * r^4 * ΔP) / (8 * η * 2L)
Q2 = (π * r^4 * ΔP) / (16 * η * L)
Q2 = Q1 / 2
Q2 = 50 cm³/s / 2
Q2 = 25 cm³/s
Therefore, the new flow rate if the length of the tube doubles is 25 cm³/s.
(d) If the radius of the tube doubles, the flow rate can be calculated using the formula:
Q = (π * (2r)^4 * ΔP) / (8 * η * L)
Q = (16π * r^4 * ΔP) / (8 * η * L)
Q2 = 2 * Q1
Q2 = 2 * 50 cm³/s
Q2 = 100 cm³/s
Therefore, the new flow rate if the radius of the tube doubles is 100 cm³/s.