This preview shows page 1. Sign up to view the full content.
Unformatted text preview: 2)1/2
1 (1 (10.43) With y2 thus known, V2 follows from the widechannel continuity relation
V1y1
y2 V2 (10.44) Finally, we can evaluate the dissipation head loss across the jump from the steadyflow
energy equation
hf E1 E2 y1 V2
1
2g V2
2
2g y2 Introducing y2 and V2 from Eqs. (10.43) and (10.44), we find after considerable algebraic manipulation that
hf (y2 y1)3
4y1y2 (10.45)  v v Equation (10.45) shows that the dissipation loss is positive only if y2 y1, which is a
requirement of the second law of thermodynamics. Equation (10.43) then requires that  eText Main Menu  Textbook Table of Contents  Study Guide 10.5 The Hydraulic Jump 681 Fr1 1.0; that is, the upstream flow must be supercritical. Finally, Eq. (10.44) shows
that V2 V1 and the downstream flow is subcritical. All these results agree with our
previous experience analyzing the normalshock wave.
The present theory is for hydraulic jumps in wide horizontal channels. For the
theory of prismatic or sloping channels see advanced texts [for example, 3, chaps.
15...
View
Full
Document
This note was uploaded on 10/27/2009 for the course MAE 101a taught by Professor Sakar during the Spring '08 term at UCSD.
 Spring '08
 Sakar

Click to edit the document details