Water flows steadily along a horizontal open channel of uniform width, over a broad-crested weir. The channel bed upstream from the weir (to the left) is d metres above the channel bed downstream from the weir (to the right), as shown in the figure below. The volume flow rate per unit width is Q = 6 m2 s-1, and upstream the depth of the water is h1 = 3m. Take the magnitude of the acceleration due to gravity as a= 10ms-2

Elements Of Electromagnetics
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Water flows steadily along a horizontal open channel of uniform width, over
a broad-crested weir. The channel bed upstream from the weir (to the left) is
d metres above the channel bed downstream from the weir (to the right), as
shown in the figure below. The volume flow rate per unit width is
Q = 6 m? s-1, and upstream the depth of the water is h1 = 3 m. Take the
magnitude of the acceleration due to gravity as g = 10 ms 2.
hi
D
p.
h2
U2
(a) Find the upstream speed u1, and show that the flow is subcritical there.
(b) Find the specific energy E (in m) for the flow upstream.
(c) By applying Bernoulli's equation along a suitable streamline, show that
the depth h2 in the downstream section of the channel satisfies the
equation
5h – (16 + 5d)h+9 = 0.
Transcribed Image Text:Water flows steadily along a horizontal open channel of uniform width, over a broad-crested weir. The channel bed upstream from the weir (to the left) is d metres above the channel bed downstream from the weir (to the right), as shown in the figure below. The volume flow rate per unit width is Q = 6 m? s-1, and upstream the depth of the water is h1 = 3 m. Take the magnitude of the acceleration due to gravity as g = 10 ms 2. hi D p. h2 U2 (a) Find the upstream speed u1, and show that the flow is subcritical there. (b) Find the specific energy E (in m) for the flow upstream. (c) By applying Bernoulli's equation along a suitable streamline, show that the depth h2 in the downstream section of the channel satisfies the equation 5h – (16 + 5d)h+9 = 0.
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