Problem #2 Bernoulli Equation Sluice pte A sluice gate is a common type of flow

Question

Problem #2 Bernoulli Equation Sluice pte A sluice gate is a common type of flow control mechanism (figures above), as well as a classical case for using Bernoulli's Equation (problem below) Water flows under the sluice gate, as shown (fig- ure on the left). Estimate the flow rate per unit width of the channel .e., Q/b, where b is the gate width). Estimate :2 as being 61% of the gate opening (see figure b, above Note that point 1 in figure (b) is at the surface of a moving channel flow NOT a very large reservior. e member to list all of your assumptions. A: Q/b = 4.61 /s 6.0 5.0 m

Explanation / Answer

Let flow rate be Q.

Let width of gate be b.

Flow area at point (1) (A1) = 5b

Flow area at point (2) (A2) = 0.61 x 0.8 x b = 0.488b

Velocity at point (1) (V1) = Q/A1= Q/5b

Velocity at point (2) (V2) = Q/A2= Q/0.488b

Elevation of point (1) from bottom (Z1) = 5 m

Elevation of point (2) from bottom (Z2) = 0.61 x 0.8 = 0.488 m

Applying Bernoulli's Principle between points (1) and (2),

V12/2g + Z1 = V22/2g + Z2

=> (Q/5b)2/2g + 5 = (Q/0.488b)2/2g + 0.488

=> (5 - 0.488) x 2g = (Q/0.488b)2 - (Q/5b)2

=> 88.53 = (Q/b)2 (1/0.4882 - 1/52)

=> (Q/b)2 = 88.53/4.159 = 21.28

=> Q/b = 4.614 m2/s

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