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# Discharge Velocity and Seepage Velocity

1 - Question

Darcy’s law describes the state of flow within individual pores.

a) True

b) False

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Answer: bExplanation: 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 - Question

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

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Answer: cExplanation: 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 - Question

The relation between discharge velocity and seepage velocity is ________

a) Vs=Ve

b) Vs=Vn

c) Vs=V/e

d) Vs=V/n

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

4 - Question

Seepage velocity is inversely proportional to hydraulic gradient.

a) True

b) False

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Answer: bExplanation: 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 - Question

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

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Answer: dExplanation: 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 - Question

The unit coefficient of permeability is ______

a) cm

b) s

c) cm/s

d) cm/s2

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Answer: cExplanation: 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 - Question

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

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Answer: bExplanation: 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 - Question

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

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Answer: bExplanation: 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 - Question

The velocity of flow is proportional to _________ according to Darcy’s law.

a) effective stress

b) hydraulic gradient

c) cohesion

d) adhesion

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

10 - Question

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

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

11 - Question

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

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Answer: bExplanation: 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 - Question

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

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Answer: bExplanation: 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.