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An open ended steel barrel of 1 m height and 1 m diameter is filled with saturated fine sand having the coefficient of permeability of 10−2 m/s. The barrel stands on a saturated bed of gravel. The time required (in seconds) for the water level in the barrel to drop by 0.75 m is
(Answer up to the nearest integer)
    Correct answer is '75'. Can you explain this answer?
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    An open ended steel barrel of 1 m height and 1 m diameter is filled w...
    Problem Statement

    An open ended steel barrel of 1 m height and 1 m diameter is filled with saturated fine sand having the coefficient of permeability of 10−2 m/s. The barrel stands on a saturated bed of gravel. The time required (in seconds) for the water level in the barrel to drop by 0.75 m is (Answer up to the nearest integer).


    Solution


    Assumptions


    • The soil is homogeneous and isotropic

    • The soil is saturated

    • The flow of water is steady

    • The flow of water is one-dimensional

    • The coefficient of permeability is constant

    • There is no air in the soil

    • The soil is incompressible



    Concepts Used


    • Darcy's Law

    • Continuity Equation



    Solution Steps

    Let us consider a control volume as shown in the figure below:

    https://edurev.in/api/screenshot/v1/2577391.png?w=800&h=600" />


    • From continuity equation, we have:


    Q = Av


    • Where,

    • Q = Rate of discharge

    • A = Cross-sectional area of the barrel

    • v = Velocity of water in the barrel



    • From Darcy's Law, we have:


    v = Kfi


    • Where,

    • Kf = Coefficient of permeability of the soil

    • i = Hydraulic gradient



    • Hydraulic gradient is given by:


    i = Δh / L


    • Where,

    • Δh = Change in water level in the barrel

    • L = Length of the barrel



    • Substituting the above equations, we get:


    Q = AKf(Δh/L)


    • Volume of water in the barrel is given by:


    V = AL


    • The rate of change of volume of water in the barrel is given by:


    dV/dt = -Q


    • Substituting the value of Q, we get:


    dV/dt =
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    Community Answer
    An open ended steel barrel of 1 m height and 1 m diameter is filled w...
    K = 10-2 m/s
    Time required for water level drop by 0.75
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    An open ended steel barrel of 1 m height and 1 m diameter is filled with saturated fine sand having the coefficient of permeability of 10−2 m/s. The barrel stands on a saturated bed of gravel. The time required (in seconds) for the water level in the barrel to drop by 0.75 m is(Answer up to the nearest integer)Correct answer is '75'. Can you explain this answer?
    Question Description
    An open ended steel barrel of 1 m height and 1 m diameter is filled with saturated fine sand having the coefficient of permeability of 10−2 m/s. The barrel stands on a saturated bed of gravel. The time required (in seconds) for the water level in the barrel to drop by 0.75 m is(Answer up to the nearest integer)Correct answer is '75'. 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 An open ended steel barrel of 1 m height and 1 m diameter is filled with saturated fine sand having the coefficient of permeability of 10−2 m/s. The barrel stands on a saturated bed of gravel. The time required (in seconds) for the water level in the barrel to drop by 0.75 m is(Answer up to the nearest integer)Correct answer is '75'. 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 An open ended steel barrel of 1 m height and 1 m diameter is filled with saturated fine sand having the coefficient of permeability of 10−2 m/s. The barrel stands on a saturated bed of gravel. The time required (in seconds) for the water level in the barrel to drop by 0.75 m is(Answer up to the nearest integer)Correct answer is '75'. Can you explain this answer?.
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