Question

Find: Label the following statements with either a “true” or a “false” and explain your reasoning (i.e. by showing the appropriate equations).

1. In TR-55, increasing the curve number always increases the predicted peak discharge
2. Increasing a culvert’s length always increases the headwater depth
3. Hydrographs predicted with the curve number method are always symmetrical triangles with a base equal to the time-of-concentration of the watershed
4. Doubling the culvert roughness will double the headwater depth under outlet control
5. In the rational method, increasing the runoff coefficient by 25 % will result in a predicted peak discharge that is increased by 25 %
6. Headwater depth always increases when the culvert inlet has a headwall (compared to a culvert without a headwall)

Answer 1

a) In TR-55, increasing the curve number always increases the predicted peak discharge.

ans: True

peak discharge is given by, Q =(P - I_a)²/(P-I_a+S) = (P–0.2S)²/(P + 0.8S)

where,

P= rainfall (inches)

I_a= initial abstraction (inches) =0.2S

S = potential maximum retention after the start of runoff (inches) = (1000/CN)-10

CN = curve number

So, we can see that increasing the CN value, the S value decreases and hence initial abstractions (I_a) also get decreases resulting into Increased value of peak discharge (Q) as evident from equation of Q.

b). Increasing a culvert’s length always increases the headwater depth.

Ans: FALSE

HW = H + h_o - S_oL

where,

HW = Headwater depth at the entrance of culvert

L = Length of culvert

S_o = Slope of the culvert pipe

h_o = (d_c+D)/2

d_c= critical depth

D = Inside diameter for circular pipe

H = head available

So, it is evident from the equation that increasing the culvert length (L) decreases the headwater depth (HW).

c). Hydrographs predicted with the curve number method are always symmetrical triangles with a base equal to the time-of-concentration of the watershed.

Ans: FALSE (Not always symmetrical, it depends upon rainfall data and initial abstractions)

d). Doubling the culvert roughness will double the headwater depth under outlet control

Ans: FALSE

HW = H + h_o - S_oL

where,

HW = Headwater depth at the entrance of culvert

L = Length of culvert

S_o = Slope of the culvert pipe

h_o = (d_c+D)/2

d_c= critical depth

D = Inside diameter for circular pipe

H = head available

So, it is evident from the equation that head water depth calculation is independent of the culvert surface roughness (n), hence headwater depth would be unaffected while doubling the surface roughness.

e). In the rational method, increasing the runoff coefficient by 25 % will result in a predicted peak discharge that is increased by 25 %

Ans: TRUE

Rational formula uses the following expression to calculate the peak discharge (Q_p)

Q_p= (1/36)*K*P_c*A

Where,

K = Runoff coefficient

P_c = Critical design rainfall intensity in cm/hr

A = Area of catchment in hectare

Q_p = Peak discharge in m³/s

It is evident from the equation that only the parameter "K" is a variable quantity and peak discharge (Q_p) is directly proportional to the runoff coefficient (K). Hence,increasing the runoff coefficient by 25 % will result in a predicted peak discharge that is increased by 25 %.