Example 19-10 (CERM page 19-21)
At a particular point in an open rectangular channel (n=0.0013, S=0.002, and W (or B) =10 ft) the flow is 250 cfs and the depth is 4.2 ft. How far from this point will the depth be 4.0 ft?
The solution has steps to follow:
Step 1: find v1, E1 and R1
Step 2: find v2, E2 and R2
Step 3: calculate R average (mean R) from R1 and R2, also calculate V average.
Step 4: apply Manning eq. to find S from n, So (given), Rave and Vave (calculated)
Then finally find L=(E1-E2)/(S-So)
In "back water curve" calculation , using direct step method (not shown in CERM, you may look at some other hydraulics books) the above procedure is repeated several times to plot the back water curve, however in the PE exam there might be a question just like the example 19-10 CERM so be prepared.
Following is the equation number 1 I wrote for the HP-33s, X is the depth at location 1 in ft, Y is the depth of location 2 in ft. Q is flow in cfs, B is bottom width in ft. Equation number 2 is the same but with V is give instead of Q. U is velocity and X is depth of flow at location 1, V is velocity and Y is depth of flow at location 1. I put in Excel spreadsheet and tested these 2 eq.'s, they gave correct answer.
One advantage of the HP-33s calculator is that you can calculate the depth at one location when Q, n, So, B, depth at the other location and distance L are given.
The manual method (4 step described above) can't (or hard to solve).
Equation 1: L=((Q/B/Y)^2/64.4+Y-(Q/B/X)^2/64.4-X)/(S-(N*(Q/B/Y+Q/B/X)/2/(1.486*(0.5*(B*Y/(2*Y+B)+B*X/(2*X+B)))^0.6667))^2)
Verification code: CK=4128 , LN=110
Equation 2: L=(V^2/64.4+Y-U^2/64.4-X)/(S-(N*(V+U)/2/(1.486*(0.5*(B*Y/(2*Y+B)+B*X/(2*X+B)))^0.6667))^2)
No verification code since I haven't entered it in the HP-33s yet, but I tested it by putting in Excel spreadsheet and it worked.
At a particular point in an open rectangular channel (n=0.0013, S=0.002, and W (or B) =10 ft) the flow is 250 cfs and the depth is 4.2 ft. How far from this point will the depth be 4.0 ft?
The solution has steps to follow:
Step 1: find v1, E1 and R1
Step 2: find v2, E2 and R2
Step 3: calculate R average (mean R) from R1 and R2, also calculate V average.
Step 4: apply Manning eq. to find S from n, So (given), Rave and Vave (calculated)
Then finally find L=(E1-E2)/(S-So)
In "back water curve" calculation , using direct step method (not shown in CERM, you may look at some other hydraulics books) the above procedure is repeated several times to plot the back water curve, however in the PE exam there might be a question just like the example 19-10 CERM so be prepared.
Following is the equation number 1 I wrote for the HP-33s, X is the depth at location 1 in ft, Y is the depth of location 2 in ft. Q is flow in cfs, B is bottom width in ft. Equation number 2 is the same but with V is give instead of Q. U is velocity and X is depth of flow at location 1, V is velocity and Y is depth of flow at location 1. I put in Excel spreadsheet and tested these 2 eq.'s, they gave correct answer.
One advantage of the HP-33s calculator is that you can calculate the depth at one location when Q, n, So, B, depth at the other location and distance L are given.
The manual method (4 step described above) can't (or hard to solve).
Equation 1: L=((Q/B/Y)^2/64.4+Y-(Q/B/X)^2/64.4-X)/(S-(N*(Q/B/Y+Q/B/X)/2/(1.486*(0.5*(B*Y/(2*Y+B)+B*X/(2*X+B)))^0.6667))^2)
Verification code: CK=4128 , LN=110
Equation 2: L=(V^2/64.4+Y-U^2/64.4-X)/(S-(N*(V+U)/2/(1.486*(0.5*(B*Y/(2*Y+B)+B*X/(2*X+B)))^0.6667))^2)
No verification code since I haven't entered it in the HP-33s yet, but I tested it by putting in Excel spreadsheet and it worked.
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