First slide

Viscosity

Question

We have two (narrow) capillary tubes T₁, and T₂ . Their lengths are l₁ and l₂and radii of cross-sections arc r₁, and r₂ respectively. The rate of flow of water under a pressure difference P through tube T₁, is 8 cm³/s. If l₁ =2 l₂ and r₁= r₂ , what will be the rate of flow when the two tubes are connected in series and pressure difference across the combination is same (P) as before?

Moderate

A

$4 {c m}^{3} / s$
B

$(16 / 3) {cm}^{3} / s$
C

$(8 / 17) {c m}^{3} / m$
D

none of the above

Solution

$Given that, V = \frac{{πPr}^{4}}{8 ηl} = 8 {cm}^{3} / s where l_{1} = l For composite tube V_{1} = \frac{{πPr}^{4}}{8 η (l + l / 2)} (∵ l_{1} = l = 2 l_{2} or l_{2} = l / 2) ∴ V_{1} = \frac{2}{3} \times (\frac{{πPr}^{4}}{8 ηl}) = \frac{2}{3} \times 8 {cm}^{3} / s = \frac{16}{3} {cm}^{3} / s$

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