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Doubt & Answer Explanation

Doubt

please discuss about the flow which occurs in capillary tubes when connected in series or parallel

Answer Explanation

If two capillaries of length l₁ and l₂ and radii r₁ and r₂ are connected in series across a constant pressure difference p, then, the fluid resistance R is given by:
R = R₁ + R₂, that is,

As the volume of liquid flowing is the same through both the capillaries, Q = Q₁ = Q₂ = p/(R₁+R₂).

If p₁ and p₂ are the individual pressure differences through both the capillaries, then, p = p₁+ p₂.

If two capillaries are connected in parallel across a constant pressure difference p, then, the fluid resistance is given by:

1/R = 1/R₁ + 1/R₂ or R = R₁R₂/R₁+R₂ where:

The volume of liquid flowing through the capillary of radius r₁ is:

Q₁ = p/R₁.

The volume of liquid flowing through the capillary of radius r₂ is:

Q₂ = p/R₂.

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