(a) The resistance to water of a capillary tube can be calculated using the formula:
R = (8 * η * L) / (π * r^4)
where R is the resistance, η is the viscosity of water, L is the length of the capillary tube, and r is the radius of the capillary tube.
Plugging in the values:
R = (8 * 0.00179 * 0.20) / (π * 0.06^4)
R ≈ 0.0028 N.s/m3
(b) The fluid flow through the capillary tube can be calculated using the formula:
Q = (π * ΔP * r^4) / (8 * η * L)
where Q is the fluid flow, ΔP is the pressure difference, η is the viscosity of water, L is the length of the capillary tube, and r is the radius of the capillary tube.
Plugging in the values:
Q = (π * 0.15 * 0.06^4) / (8 * 0.00179 * 0.20)
Q ≈ 0.000067 m3/s
(c) To calculate the pressure difference that gives a fluid flow of 0.5 cm3/s, we rearrange the formula:
ΔP = (Q * 8 * η * L) / (π * r^4)
Plugging in the values:
ΔP = (0.0005 * 8 * 0.00179 * 0.20) / (π * 0.06^4)
ΔP ≈ 0.28 mmH2o