5 the hydraulic jump 681 fr1 10 that is the upstream

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Unformatted text preview: and 16]. EXAMPLE 10.7 Water flows in a wide channel at q 10 m3/(s m) and y1 1.25 m. If the flow undergoes a hydraulic jump, compute (a) y2, (b) V2, (c) Fr2, (d) hf, (e) the percentage dissipation, (f) the power dissipated per unit width, and (g) the temperature rise due to dissipation if cp 4200 J/(kg K). Solution Part (a) The upstream velocity is 10 m3/(s m) 1.25 m q y1 V1 8.0 m/s The upstream Froude number is therefore V1 (gy1)1/2 Fr1 8.0 [9.81(1.25)]1/2 2.285 From Fig. 10.12 this is a weak jump. The depth y2 is obtained from Eq. (10.43): 2y2 y1 or Part (b) 1 1 21 y2 y (5.54) V1y1 y2 V2 (gy2)1/2 v v Hence | Ans. (a) 8.0(1.25) 3.46 2.89 m/s Ans. (b) 2.89 [9.81(3.46)]1/2 0.496 Ans. (c) (3.46 1.25)3 4(3.46)(1.25) 0.625 m Ans. (d) The percentage dissipation relates hf to upstream energy E1 | 3.46 m As expected, Fr2 is subcritical. From Eq. (10.45) the dissipation loss is hf Part (e) (1.25)(5.54) The downstream Froude number is Fr2 Part (d) 1 2 5.54 From Eq. (10.44) the downstream velocity is V2 Pa...
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This note was uploaded on 10/27/2009 for the course MAE 101a taught by Professor Sakar during the Spring '08 term at UCSD.

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