# Environmental Engineering Questions and Answers – Filtration Hydraulics

This set of Environmental Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Filtration Hydraulics”.

1. The head loss through the bed of solids of the filter can be determined by __________
a) Carmen-Kozney equation
b) Rose equation
c) Carmen-Kozney and Rose equation
d) Charles equation

Explanation: The head loss through the bed of solids of the filter can be determined by both Carmen-Kozney and Rose equation where two cases are considered, one for homogeneous mixed bed and other for stratified bed.

2. Which of the following has the highest shape factor as stated by Carmen?
a) Ottawa sand
b) Pulverized coal
c) Rounded coal
d) Angular sand

Explanation: The shape factor as stated by Carmen is 0.95 for Ottawa sand, 0.73 for pulverized coal and angular sand and 0.82 for rounded sand.

3. Which of the following is the expression of the Carmen equation where symbols have their usual meanings?
a) hf = f* (L/(s *d)) * ((1-e)/e3) * (v2/g)
b) hf = f* (L/(s *d)) * ((1-e)/e3) * (v/g)
c) hf = f* (L/(s *d)) * ((1-e)/e) * (v2/g)
d) hf = f* (L/(s *d)) * ((1-e)/e2) * (v2/g)

Explanation: The expression of the Carmen equation is given by hf = f* (L/(s *d)) * ((1-e) /e3) * (v2/g) where hf =head loss, d= diameter of pipe. L= length of pipe and v=approach velocity.

4. Which of the following represents the correct relation between dimensionless friction factor f and Reynolds number?
a) f = 150* ((1-e) /R2) + 1.75
b) f = 150* ((1-e) /R) +1.75
c) f = 150* ((1-e) /R3) + 1.75
d) f = 150* ((1-e2) /R) + 1.75

Explanation: The correct relation between dimensionless friction factor and Reynolds number is given by f = 150* ((1-e) /R) + 1.75 Where R is the Reynolds number and the expression (1-e) represents the volume of solids.

5. Which of the following is the expression of the Rose equation where symbols have their usual meanings?
a) hf = f* (L/(s *d)) * ((1-e) /e3) * (v2/g)
b) hf = f* (L/(s *d)) * ((1-e) /e3) * (v/g)
c) hf = f* (L/(s *d)) * ((1-e) /e4) * (v2/g)
d) hf = f* (L/(s *d)) * ((1-e) /e2) * (v2/g)

Explanation: The expression of the Rose equation is given by hf = f* (L/(s *d)) * ((1-e) /e3) * (v2/g) where hf = head loss, d = diameter of pipe. L = length of pipe and v=approach velocity and f = 1.067CD, Where CD is the coefficient of drag.

6. When the Reynolds number is greater than 1.9 but less than 500, the coefficient of drag CD is?
a) CD = 24/R
b) CD = R/24
c) CD = 18.5/R0.6
d) CD = R0.6/18.5

Explanation: When the Reynolds number is greater than 1.9 but less than 500, the coefficient of drag CD is CD = 18.5/R0.6 where R is the Reynolds number.

7. The value of Reynolds number R is 1.5. The coefficient of drag is?
a) 8
b) 10
c) 12
d) 16

Explanation: When R<1.9, the value of the coefficient of drag = 24/R
R=1.5, the coefficient of drag = 24/1.5 = 16.

8. Rose equation is valid for beds in which voids are clear and unobstructed.
a) True
b) False

Explanation: Rose equation is valid for beds in which voids are clear and unobstructed though during continues filtration, voids get clogged and head loss goes on increasing.

9. When does the particle become suspended in an expanded bed?
a) When superficial velocity is greater than critical velocity
b) When superficial velocity is less than critical velocity
c) When superficial velocity is equal to critical velocity
d) When superficial velocity is constant

Explanation: During back washing, the bed remains fixed at low fluid velocity and as the superficial velocity increases, the lighter particles move upward and when this velocity equals the critical velocity, the particle becomes suspended.

10. The superficial velocity in a stratified bed is equal to __________
a) Terminal settling velocity
b) Terminal settling velocity * porosity
c) Terminal settling velocity * (porosity)2
d) Terminal settling velocity * (porosity)4.5

Explanation: A stratified bed having a non uniform sized particles are completely fluidized when for the largest particle, the superficial velocity v = vs * e4.5 where vs is the terminal settling velocity and e is the porosity.

11. Carmen-Kozney equation has been derived using which of the following equation?
a) Cole brook white equation
b) Bernoulli equation
c) Darcy Weisbach equation
d) Swamee jain equation

Explanation: Carmen-Kozney equation has been derived using Darcy Weisbach equation which is given by h = f*l*v2/(g*D) Where h is the head loss, D is the diameter of pipe, v is the velocity of the particle and f is the dimensionless friction factor.

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