Rapidly Varying Flow - Hydraulic Jumps
Example: The
figure below shows the flow under a sluice gate where y1 = 2 inches and V1
= 17ft/sec. Determine the depth of flow downstream of
the jump and the head loss across
the jump. Strategy: Calculate the Froude Number at the upstream
station. If Fr1 > 1, then the flow is unstable
and results in energy dissipation producing a hydraulic jump. Then apply the following relations
to determine the downstream depth and energy loss across the jump: ( y2 /y1
) =
[ -1 + √( 1 + 8 Fr12)]
/ 2 and hL / y1 = Fr12/2 [ 1 – (y1/y2)2]
+ [1– (y2/ y1)]
Fr1 =
17/√ 32.2)(2/12) = 7.3
(therefore supercritical flow upstream) ( y2 /y1 ) = [
-1 +
√( 1 + 8 (7.3)2)] / 2 = 9.88 y2 =
19.8 inches (result) Next calculate the head loss. y2 /y1 =
9.88 , y1/y2 =
0.1011 So hL / y1 =
7.32/2 [ 1 – (0.1011)2]
+ [1– 9.4)] = 17.76 hL =
35.5 in or
2.96 ft (result) Initial
Specific energy = y1 + V12/2g =
2/12 + (17)2/64.4
= 4.65 ft hL
/ E1 = 2.96/4.65
= 0.64 Hydraulic jump dissipates 64% of incoming
energy. Click
here to examine the specific energy diagram for this example. |
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