The SB River has two tributaries. The Upper SB has a discharge 400
meters3/second and a velocity of 20 meters/second. The Main SB has a
velocity of 35 meters/second and a width of 5 meters. The Lower SB has
a width of 3 meters and a velocity of 15 meters/second. Assume the
profile of all three branches is a filled half cylinder. Fill in the
table below.

Branch	Velocity (m/s)	Discharge (m3/s)	Width (m)
Main SB	35		5
Upper SB	20	400	
Lower SB	15		3

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Clarification of Question by goog34-ga on 14 Dec 2004 13:23 PST

You ar right, there should be in 5 in the width column of the main
branch.  Please advice with the right answer.

There is something wrong in your question as posted.

a)If a river is a tributary to another river, then the tributary
discharges into the other river.
So, Upper and Lower SB should discharge into the Main SB river.
Then, Physics or no Physics, common sense says that Discharge of Upper
SB plus Discharge of Lower SB equals Discharge of Main SB. (You did
not mention any loss by leaks, evaporation, spillways, outlets, etc.)

b) If the 3 river profiles are all filled half-cylinders, then each
cross section area is a half-circle or half-moon, which is Area =
(1/2)[pi*{diameter^2)/4] = (pi/8)(diam^2).
Also, the width of the river is the diameter of the cylinder/circle. So,
Area = (pi/8)(width^2)

c)Discharge = velocity*area
For Upper SB, D_u = 400 cu.m./sec  ----given.
For Lower SB, D_L = (15)*[(pi/8)(3^2)] = 53 cu.m./sec
For Main SB, D_m = (35)*[(pi/8)(5^2)] = 344 cu.m./sec

Is 400 + 53 = 344?
No.

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Approach your posted question in other ways, the given data still won't match.

Did you then post the correct question?

No, it is not about the location of the data in the table as posted.
The 5 is the width of SB Main as mentioned earlier.

The table shows 3 variables per river branch: discharge, velocity and
width. Those 3 variables are related to each other by the equation:
discharge = (velocity)*[(pi/8)(width^2)]

In that equation, if two of the 3 variables are known, the third
variable can be solved easily.
In the table, for each of the river branches, exactly two of the 3
variables are given. So you can easily solve for all the missing third
variables.
Then, check your answers against the equation:
(discharge Of Upper Branch) + (discharge of Lower branch) = discharge
of Main branch.
If that is not satisfied, then your answers are wrong.

Review again the given data. Correct it, and solve your problem.
(Forget about Physics. It is only simple Algebra.)