Solution Assignment (6)

Flow in Natural Drainage Streams ( Open Channels ) The shown figure below, is a plan view of a storm sewer system

draining three subbasins. Use the Rational method to determine the

peak discharge in each pipe and size of pipe assuming the pipes flow

full and constant mean velocity of (1.5 m/s = 5 ft/s). Perform the

calculations for a storm assuming duration = time of concentration.

Solution

basin Area

(acre

)

K tc = t I

(in/hr)

Q

(cfs)

A 6.0 0.6 20 5.26 6*0.6*5.26 = 19 cfs

B 4.0 0.8 10 7.02 4*0.8*7.02 = 22.5 cfs

C 4.5 0.8 15 5.96 4.5*0.8*5.96 = 21.5

cfs

Pipe 1 Pipe 2 Pipe 3

QA = 19.0 cfs QC = 21.5 cfs QA + QC + QB = 63 cfs

A = Q/V = 19/5 = D2/4

D = 2.2 ft

A = Q/V = 21.5/5 = D2/4

D = 2.34 ft

A = Q/V = 63/5 = D2/4

D = 4 ft

Important Comment

For pipes or open channel used for draining a catchment area

1- Case (1) V is given,

For pipe A = Q/V = D2/4, estimate D

For open channel A = Q/V = y (b+zy) and for rectangular section

A = b*y , b/y = given value = 2 for example, estimate y, b

2- Case (2) V is not given,

For pipe, data of n, S should be given to apply Manning Equation to estimate D.

Q = (1/n) A5/3/P2/3 S0.5 where, A = D2/4, and P = D

For open channel , data of [n, S, z & b/y = given value] should be given to apply

Manning Equation to estimate y & b

Q = (1/n) A5/3/P2/3 S0.5

Where A = y(b+zy), P = b +2y(1+z2)0.5