Civil Engineering (CE) Exam  >  Civil Engineering (CE) Questions  >   A water filtration unit is made of uniform-s... Start Learning for Free
A water filtration unit is made of uniform-size sand particles of 0.4 mm, diameter with a shape factor of 0.84 and specific gravity of 2.55. The depth of the filter bed is 0.70 m and the porosity is 0.35. The filter bed is to be expanded to a porosity of 0.65 by hydraulic backwash. If the terminal settling velocity of sand particles during backwash is 4.5 cm/s, the required backwash velocity is
  • a)
    0.75 cm/s
  • b)
    5.79 × 10-3 m/s
  • c)
    0.69 cm/s
  • d)
    6.35 × 10-3 m/s
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A water filtration unit is made of uniform-size sand particles of 0.4...
To determine the required backwash velocity, we need to consider the properties of the sand particles and the desired porosity of the filter bed.

Given data:
- Diameter of sand particles (d): 0.4 mm
- Shape factor (α): 0.84
- Specific gravity (G): 2.55
- Depth of filter bed (H): 0.70 m
- Initial porosity (n1): 0.35
- Desired porosity (n2): 0.65
- Terminal settling velocity during backwash (Vt): 4.5 cm/s

Let's calculate the void ratio (e) of the filter bed using the initial porosity:

e = (1 - n1) / n1 = (1 - 0.35) / 0.35 = 1.857

Next, we can calculate the void ratio (e2) required to achieve the desired porosity:

e2 = (1 - n2) / n2 = (1 - 0.65) / 0.65 = 0.538

Now, we can calculate the settling velocity (Vs) of the sand particles using the shape factor:

Vs = Vt / α = 4.5 cm/s / 0.84 = 5.357 cm/s

To determine the required backwash velocity (Vb), we can use the following equation:

Vb = (Vs * (e - e2)) / (G * H * (1 - n2))

Substituting the values we have:

Vb = (5.357 cm/s * (1.857 - 0.538)) / (2.55 * 0.70 m * (1 - 0.65))
= 0.0635 m/s

Converting the backwash velocity to cm/s:

Vb = 0.0635 m/s * 100 cm/m
= 6.35 cm/s

Therefore, the required backwash velocity is 6.35 cm/s, which corresponds to option D.
Free Test
Community Answer
A water filtration unit is made of uniform-size sand particles of 0.4...
For expanding bed,
Porosity (n) =
Where, VB = backwashing velocity
VC = Setting velocity during backwashing
Given, Porosity (n) = 0.65
VS = 4.5 cm/sec
VB = 4.5 × (0.65)1/0.22 = 0.635 cm/sec = 0.00635 m/sec
VB = 6.35 × 10-3 m/sec
Explore Courses for Civil Engineering (CE) exam

Similar Civil Engineering (CE) Doubts

Top Courses for Civil Engineering (CE)

A water filtration unit is made of uniform-size sand particles of 0.4 mm, diameter with a shape factor of 0.84 and specific gravity of 2.55. The depth of the filter bed is 0.70 m and the porosity is 0.35. The filter bed is to be expanded to a porosity of 0.65 by hydraulic backwash. If the terminal settling velocity of sand particles during backwash is 4.5 cm/s, the required backwash velocity isa)0.75 cm/sb)5.79 × 10-3 m/sc)0.69 cm/sd)6.35 × 10-3 m/sCorrect answer is option 'D'. Can you explain this answer?
Question Description
A water filtration unit is made of uniform-size sand particles of 0.4 mm, diameter with a shape factor of 0.84 and specific gravity of 2.55. The depth of the filter bed is 0.70 m and the porosity is 0.35. The filter bed is to be expanded to a porosity of 0.65 by hydraulic backwash. If the terminal settling velocity of sand particles during backwash is 4.5 cm/s, the required backwash velocity isa)0.75 cm/sb)5.79 × 10-3 m/sc)0.69 cm/sd)6.35 × 10-3 m/sCorrect answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A water filtration unit is made of uniform-size sand particles of 0.4 mm, diameter with a shape factor of 0.84 and specific gravity of 2.55. The depth of the filter bed is 0.70 m and the porosity is 0.35. The filter bed is to be expanded to a porosity of 0.65 by hydraulic backwash. If the terminal settling velocity of sand particles during backwash is 4.5 cm/s, the required backwash velocity isa)0.75 cm/sb)5.79 × 10-3 m/sc)0.69 cm/sd)6.35 × 10-3 m/sCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A water filtration unit is made of uniform-size sand particles of 0.4 mm, diameter with a shape factor of 0.84 and specific gravity of 2.55. The depth of the filter bed is 0.70 m and the porosity is 0.35. The filter bed is to be expanded to a porosity of 0.65 by hydraulic backwash. If the terminal settling velocity of sand particles during backwash is 4.5 cm/s, the required backwash velocity isa)0.75 cm/sb)5.79 × 10-3 m/sc)0.69 cm/sd)6.35 × 10-3 m/sCorrect answer is option 'D'. Can you explain this answer?.
Solutions for A water filtration unit is made of uniform-size sand particles of 0.4 mm, diameter with a shape factor of 0.84 and specific gravity of 2.55. The depth of the filter bed is 0.70 m and the porosity is 0.35. The filter bed is to be expanded to a porosity of 0.65 by hydraulic backwash. If the terminal settling velocity of sand particles during backwash is 4.5 cm/s, the required backwash velocity isa)0.75 cm/sb)5.79 × 10-3 m/sc)0.69 cm/sd)6.35 × 10-3 m/sCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE). Download more important topics, notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free.
Here you can find the meaning of A water filtration unit is made of uniform-size sand particles of 0.4 mm, diameter with a shape factor of 0.84 and specific gravity of 2.55. The depth of the filter bed is 0.70 m and the porosity is 0.35. The filter bed is to be expanded to a porosity of 0.65 by hydraulic backwash. If the terminal settling velocity of sand particles during backwash is 4.5 cm/s, the required backwash velocity isa)0.75 cm/sb)5.79 × 10-3 m/sc)0.69 cm/sd)6.35 × 10-3 m/sCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of A water filtration unit is made of uniform-size sand particles of 0.4 mm, diameter with a shape factor of 0.84 and specific gravity of 2.55. The depth of the filter bed is 0.70 m and the porosity is 0.35. The filter bed is to be expanded to a porosity of 0.65 by hydraulic backwash. If the terminal settling velocity of sand particles during backwash is 4.5 cm/s, the required backwash velocity isa)0.75 cm/sb)5.79 × 10-3 m/sc)0.69 cm/sd)6.35 × 10-3 m/sCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for A water filtration unit is made of uniform-size sand particles of 0.4 mm, diameter with a shape factor of 0.84 and specific gravity of 2.55. The depth of the filter bed is 0.70 m and the porosity is 0.35. The filter bed is to be expanded to a porosity of 0.65 by hydraulic backwash. If the terminal settling velocity of sand particles during backwash is 4.5 cm/s, the required backwash velocity isa)0.75 cm/sb)5.79 × 10-3 m/sc)0.69 cm/sd)6.35 × 10-3 m/sCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of A water filtration unit is made of uniform-size sand particles of 0.4 mm, diameter with a shape factor of 0.84 and specific gravity of 2.55. The depth of the filter bed is 0.70 m and the porosity is 0.35. The filter bed is to be expanded to a porosity of 0.65 by hydraulic backwash. If the terminal settling velocity of sand particles during backwash is 4.5 cm/s, the required backwash velocity isa)0.75 cm/sb)5.79 × 10-3 m/sc)0.69 cm/sd)6.35 × 10-3 m/sCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice A water filtration unit is made of uniform-size sand particles of 0.4 mm, diameter with a shape factor of 0.84 and specific gravity of 2.55. The depth of the filter bed is 0.70 m and the porosity is 0.35. The filter bed is to be expanded to a porosity of 0.65 by hydraulic backwash. If the terminal settling velocity of sand particles during backwash is 4.5 cm/s, the required backwash velocity isa)0.75 cm/sb)5.79 × 10-3 m/sc)0.69 cm/sd)6.35 × 10-3 m/sCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
Explore Courses for Civil Engineering (CE) exam

Top Courses for Civil Engineering (CE)

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev