Question

Label the following statements with either a “true” or a “false” and explain your reasoning (i.e. by showing the appropriate equations). In the rational method, increasing the watershed slope decreases the predicted runoff volume

1. In the curve number method, increasing the channel slope increases the predicted peak discharge
2. Culvert roughness has no effect on headwater depth under inlet control
3. Increasing tailwater depth increases headwater depth under outlet control
4. If the time-of-concentration includes shallow concentrated flow, increasing the slope of that flow path will increase the predicted peak discharge
5. For a given discharge, increasing Manning’s roughness coefficient for a channel will increase the flow depth
6. In the curve number method, doubling the 24 hour rainfall amount for the design storm doubles the predicted runoff volume
7. Iteration is required to compute the time-of-concentration in the curve number method

Answer 1

Ans) False because according to rational method,

Q = K i A ,

Where, K = coefficient of runoff which is directly proportion to runoff (Q). The value of 'K' depends on slope and type of soil surface. Higher the value of slope, higher will be the runoff coefficient and higher will be runoff. Therefore increase in watershed slope increase the predicted runoff

Ans) True , increase in slope increases the predicted the peak discharge in curve number method because

Q_p = q_u A Q F

where, q_u = unit peak discharge

A = area of watershed

Q =runoff

F = adjustment factor

According to curve number method, runoff Q is proportional to Curve number. Also, curve number increase with increasing slope..Hence, higher the slope, higher will be curve number and higher will be peak discharge

Ans) False, head water depth in inlet control given by

y_h = y_c + V²/2g[ D (C₁ 4Q/ D^2.5)^C₂ + C₃S

In above formula, C1 , C2 and C3 are factors depend on roughness of culvert

Ans) True, increase in tailwater depth increase the headwater depth because in outlet control culvert, water enter in culvert faster then it can release , so if tailwater dept is high, it means that headwater depth is also high

Ans) True, time of concentration is inversely proportional to slope.Increase the slope reduce the time of concentration which increase the velocity.Higher the velocity higher will be discharge.

t_c = L / 3600KS^0.50 , where S is slope

Ans) False, increase in Manning roughness coefficient decrease the flow depth because Manning roughness is inversely proportional to discharge :

Q = (1/N)R^2/3S^1/2

Ans) True, higher the value of rainfall intensity higher will be discharge because:

Q = (P - i)² / (P - i + S)

Ans) False, time of concentration according to curve number can be given by :

t_c = 1.67L^0.80 [( 1000 /CN) - 9] ^0.7 / 1900 S^0.5

It is not an iterative process