# Soil Mechanics Questions and Answers – Permeability – Discharge Velocity and Seepage Velocity

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This set of Soil Mechanics Multiple Choice Questions & Answers (MCQs) focuses on “Discharge Velocity and Seepage Velocity”.

1. Darcy’s law describes the state of flow within individual pores.
a) True
b) False

Explanation: Darcy’s law in no way describes the state of flow within individual pores. Darcy’s law represents the statistical macroscopic equivalent of the Navier-Strokes equations of motion for various viscous flow of ground water.

2. In the definition of the seepage velocity, the cross-sectional area of the voids is taken as _______ to the direction of flow.
a) parallel
b) opposite
c) perpendicular
d) tangential

Explanation: The seepage velocity is defined as the rate of discharge of percolating water per unit cross-sectional area of voids perpendicular to the direction of the flow.

3. The relation between discharge velocity and seepage velocity is ________
a) Vs=Ve
b) Vs=Vn
c) Vs=V/e
d) Vs=V/n

Explanation: Since the discharge is equal,
Q=VA=VsAV
Vs=VA/AV
Since AV/A=VV/V=n
∴ Vs=V/n.

4. Seepage velocity is inversely proportional to hydraulic gradient.
a) True
b) False

Explanation: From Darcy’s law, the discharge velocity is proportional to the hydraulic gradient. Since discharge velocity is also proportional to seepage velocity, we have seepage velocity proportional to the hydraulic gradient.

5. The coefficient of permeability of clean gravel is _________
a) 1*10-6 and smaller
b) 5*10-4 – 1*10-5
c) 1 – 1*10-2
d) 1 and greater

Explanation: The coefficient of permeability of clay, silt and clean coarse sand are 1*10-6 and smaller, 5*10-4 – 1*10-5 and 1 – 1*10-2 respectively.

6. The unit coefficient of permeability is ______
a) cm
b) s
c) cm/s
d) cm/s2

Explanation: Consider velocity in cm/s,
The hydraulic gradient i=(h/L), where both h and L are in cm.
By Darcy’s law,
V=ki
K=v/i
Considering its units,
K=(cm/s)/(cm/cm)
∴ K=(cm/s)
Hence, coefficient of permeability has same units as velocity.

7. If the discharge velocity is 4*10-7cm/s and the porosity is 33%, then the seepage velocity will be _______
a) 18*10-7cm/s
b) 12*10-7cm/s
c) 6*10-7cm/s
d) 3*10-7cm/s

Explanation: Given,
discharge velocity V=4*10-7cm/s
porosity n=33%=0.33
seepage velocity Vs=V/n=(4*10-7)/0.33
∴ Vs=12*10-7cm/s.

8. If the soil has discharge velocity is 9*10-7cm/s and the voids ratio of 0.5, then the seepage velocity will be _______
a) 18*10-7cm/s
b) 27*10-7cm/s
c) 16*10-7cm/s
d) 13*10-7cm/s

Explanation: Given,
discharge velocity V=9*10-7cm/s
voids ratio e= 0.5
n=e/(1+e)=0.5/(1+0.5)=0.33
Vs=V/n=(9*10-7)/0.33
∴ Vs=27*10-7cm/s.

9. The velocity of flow is proportional to _________ according to Darcy’s law.
a) effective stress
c) cohesion

Explanation: The Darcy’s law states that the rate of flow is proportional to the hydraulic gradient.
V=q/A=ki
where, V=velocity
K= coefficient of permeability.

10. The relationship between coefficient of permeability and coefficient of percolation is ______
a) kp=kn
b) kp=ke
c) kp=k/e
d) kp=k/n

Explanation: From Darcy’s law, V=ki
And Vs=kpi
∴ Vs/V=kp/k=1/n
∴ kp=k/n.

11. If the coefficient of permeability of soil is 9*10-7cm/s and porosity is 0.33, then its coefficient of percolation is ______
a) 8*10-7cm/s
b) 27*10-7cm/s
c) 26*10-7cm/s
d) 13*10-7cm/s

Explanation: Given,
coefficient of permeability k=9*10-7cm/s
porosity n=0.33
coefficient of percolation kp=k/n=(9*10-7)/0.33
∴ kp=27*10-7cm/s.

12. If the coefficient of percolation is 18*10-7cm/s and void ratio is 0.5, then the coefficient of permeability k is _________
a) 26*10-7cm/s
b) 6*10-7 cm/s
c) 3*10-7cm/s
d) 13*10-7cm/s

Explanation: Given,
coefficient of percolation kp=18*10-7cm/s
void ratio e= 0.5
n=e/(1+e)=0.5/(1+0.5)=0.33
since kp=k/n
k= kp*n
k=(18*10-7)*0.33
k=6*10-7 cm/s.

Sanfoundry Global Education & Learning Series – Soil Mechanics.

To practice all areas of Soil Mechanics, here is complete set of 1000+ Multiple Choice Questions and Answers.