Content deleted Content added
m spelling |
m →Example problem: wikilinked Conjugate depth Tags: Mobile edit Mobile web edit Advanced mobile edit |
||
| (One intermediate revision by one other user not shown) | |||
Line 11:
:<math>H = z+y+\frac{v^2}{2g}</math> <big>'''Equation 1'''</big>
For a given flow rate and channel geometry, there is a relationship between flow depth and total energy. This is illustrated below in the plot of energy vs. flow depth, widely known as an E-y diagram. In this plot, the depth where the minimum energy occurs is known as the critical depth. Consequently, this depth corresponds to a [[Froude Number]] <math>(F_n)</math> of 1. Depths greater than critical depth are considered “subcritical” and have a Froude Number less than 1, while depths less than critical depth are considered supercritical and have Froude Numbers greater than 1.
:<math>F_n=\frac{v}{(g\frac{A}{B})^{0.5}}</math> <big>'''Equation 2'''</big>
Line 71:
Using Figure 3 and knowledge of the upstream and downstream conditions and the depth values on either side of the gate, a general estimate of the profiles upstream and downstream of the gate can be generated. Upstream, the water surface must rise from a normal depth of 0.97 m to 9.21 m at the gate. The only way to do this on a mild reach is to follow an M1 profile. The same logic applies downstream to determine that the water surface follows an M3 profile from the gate until the depth reaches the [[conjugate depth]] of the normal depth at which point a hydraulic jump forms to raise the water surface to the normal depth.
'''Step 4:''' Use the Newton Raphson Method to solve the M1 and M3 surface water profiles. The upstream and downstream portions must be modeled separately with an initial depth of 9.21 m for the upstream portion, and 0.15 m for the downstream portion. The downstream depth should only be modeled until it reaches the conjugate depth of the normal depth, at which point a hydraulic jump will form. The solution presented explains how to solve the problem in a spreadsheet, showing the calculations column by column. Within Excel, the goal seek function can be used to set column 15 to 0 by changing the depth estimate in column 2 instead of iterating manually.
| |||