1). (a) Explain the terms \'Specific Energy\' and \'Alternate Depths\' in the co

Question

1). (a) Explain the terms 'Specific Energy' and 'Alternate Depths' in the context of open channel flow. (15 marks)

(b) Flow in a full, long, semi-circular channel of width 2m, is observed to be extremely sensitive to long disturbances suggesting that the flow is nearly critical. Estimate the
flow.(5 marks)

2).(a) In slope stability analysis, it is sometimes necessary to refer to the polygon of forces. What is meant by this term and what does it look like for Bishop's method of analysis?
(10 marks)

(b) An element of soil is located at a depth of 10m below the surface of a soft silty clay. If the water table is lowered from the ground surface to a depth of 2 metres below the
ground surface, what will be the change in the vertical effective stress acting on the element? Assume that the soil has a saturated unit weight of20kN/m3• (5 marks)

( c) What will be the likely effect of this change in effective stress? (5 marks)

Explanation / Answer

Answer 1(a)

Specific energy is the energy head relative to the bottom of channel in an open channel flow. For open channel flow the pressure at top is atmospheric pressure and applying bernaullis equation at any section in open channel flow energy head = velocity head + datum head ( pressure head not taken into account)

Specific Energy head = v^2/2g + y ( where y is height from channel bottom )

Alternate depths : If we plot depth of flow vs specific energy graph then the graph is assymptotic at E= y and X axis ( particularly for open channel flow in rectangular channel). Now in the same graph we will have two different values of depth of flow for same value of specific energy. These depths of flow are known as alternate depths.

Answer 1(b)

For semicircular channel of width or diameter 2 m thus B=2 m

For open channels B = gA^3/Q^2

Thus Q= sqrt( 9.81*(3.142*2*2/8)^3/2) = 4.361 m3/s flow at critical depth or critical flow.

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