Soil Mechanics Questions and Answers – Poiseuille’s Law

This set of Soil Mechanics Multiple Choice Questions & Answers (MCQs) focuses on “Poiseuille’s Law”.

1. For flow of water in tube, the velocity at surface is ___________
a) zero
b) equal to velocity at 1/3 of diameter
c) equal to velocity at 1/2 of diameter
d) equal to velocity at centre
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2. In Poiseuille’s law of flow, the variation of the velocity is given by _______
a) v = \(\frac{hγ_w}{4ηL}(r^2-R^2)\)
b) v = \(\frac{hγ_w}{14ηL}(R^2-r^2)\)
c) v = \(\frac{hγ_w}{4ηL}(R^2-r^2)\)
d) v = \(\frac{hγ_w}{8ηL}(R^2-r^2)\)
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Answer: c
Explanation: Consider a capillary tube of length L and radius R.

In equilibrium the sum of the forces is zero,
πr²h₁γ_w– πr²h₁γ_w-τ(2πrL)=0
on simplification, \(dv=-\frac{hγ_w}{2ηL}rdr\)
on integration,
\(v =- \frac{hγ_w}{4ηL}r^2 + C \,where\, C=\frac{hγ_w}{4ηL} R^2\)
∴ \(v = \frac{hγ_w}{4ηL}(R^2-r^2).\)

3. The velocity of flow of water at the centre of tube is _______ when the head is 0.1m, η=8.9*10^-3 dynes-s/cm², γ_w=1 g/cm³, the length is 10m and the diameter is 20cm.
a) 20 cm/s
b) 22 cm/s
c) 28 cm/s
d) 30 cm/s
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4. The quantity of water flowing in thin cylindrical sheet of thickness dr is ____________
a) \(dq=\frac{hγ_w}{4ηL}(R^2-r^2)2πrdr\)
b) \(dq=\frac{hγ_w}{4ηL}(R^2-r^2)4πrdr\)
c) \(dq=\frac{hγ_w}{4ηL}(R^2-r^2)8πrdr\)
d) \(dq=\frac{hγ_w}{4ηL}(R^2-r^2)12πrdr\)
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5. The total quantity of water flowing through the capillary tube is given by _________
a) \(q=\frac{hγ_w}{4ηL} R^2 \)
b) \(q=\frac{hγ_w}{4ηL} R^4\)
c) \(q=\frac{hγ_w}{8ηL} R^2\)
d) \(q=\frac{hγ_w}{8ηL} πR^4\)
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6. The total quantity of water with respect to the hydraulic gradient flowing through the capillary tube is given by _________
a) \( q=\frac{hiγ_w}{4ηL} R^2 \)
b) \( q=\frac{hγ_w}{4ηL} R^4/i\)
c) \( q=\frac{iγ_w}{8η} π R^2\)
d) \( q=\frac{iγ_w}{8η} πR^4\)
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7. The average velocity of the tube of area a is given by _________
a) \(v_{av}=\frac{iγ_w}{8ηπ}a \)
b) \(v_{av}=\frac{\frac{iγ_w}{8ηπ}}{a}\)
c) \(v_{av}=\frac{iγ_w}{2ηπ}a\)
d) \(v_{av}=\frac{\frac{iγ_w}{4ηπ}}{a}\)
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8. The hydraulic radius R_H is the ratio of the area of the tube to its volume.
a) True
b) False
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9. The hydraulic radius R_H of circular tube is given by ________
a) R_H=R/4
b) R_H=R/6
c) R_H=R/2
d) R_H=R/12
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10. The hydraulic radius R_H is related with the voids ratio as ________
a) R_H=V_s/eA_s
b) R_H=eV_sA_s
c) R_H=e/A_sV_s
d) R_H=eV_s/A_s
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11. The quantity of flow for circular tube with respect to the hydraulic radius is given by ________
a) \(q=\frac{1}{2}\frac{γ_w R_H^2}{η} \)
b) \(q=\frac{1}{2}\frac{γ_w R_H^2}{η}ia\)
c) \(q=\frac{1}{2}\frac{γ_w R_H^2}{η}i\)
d) \(q=\frac{1}{2}\frac{γ_w R_H^2}{η}a \)
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12. The relationship between the quantity of flow with respect to the hydraulic radius and the voids ratio is given by ________
a) \(q=\frac{γ_w R_H^2}{η}\frac{e}{1+e}iA\)
b) \(=C_S\frac{γ_w R_H^2}{η}\frac{e}{1+e}\)
c) \(=C_S\frac{γ_w R_H^2}{η}iA\)
d) \(=C_S\frac{γ_w R_H^2}{η}\frac{e}{1+e}iA\)
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Sanfoundry Global Education & Learning Series – Soil Mechanics.

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