GATE CE 2014 Set 2 — Question 39
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Engineering Mathematics → Ordinary Differential Equations → Boundary Value Problems
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Question
Water is flowing at a steady rate through a homogeneous and saturated horizontal soil strip of 10 m length. The strip is being subjected to a constant water head () of 5 m at the beginning and 1 m at the end. If the governing equation of flow in the soil strip is (where is the distance along the soil strip), the value of (in m) at the middle of the strip is ___________
Correct answer
3 to 3
Solution
The governing equation is .
Integrating once:
Integrating again:
Applying boundary conditions:
At , m .
At m, m .
So, the equation for head is .
At the middle of the strip, m:
m.
Integrating once:
Integrating again:
Applying boundary conditions:
At , m .
At m, m .
So, the equation for head is .
At the middle of the strip, m:
m.
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