Snyder Unit Hydrograph (1938)

Snyder developed the synthetic Unit Hydrograph theory in 1938 and it was modified later by more researchers. This method is applicable to the basins ranging in size from 10 to 10,000 square miles. Snyder relation is as follows:
t_l=C_t(LL_c)^0.3
where,
t_l=basin lag time (hr)
C_t=coefficient for representating differences in types and locations of streams, generally ranging from 1.8 to 2.2.(although several other values outside this range are documented).Steeper slopes tend to have lower values.
L=length of the main channel from the outlet to the watershed divide. (Note here that the length is upto the watershed divide and not where the stream begins)- mile.
L_c=length of the main channel from the outlet to the center of gravity of the basin. (mile)
The peak discharge of the unit hydrograph is given as:
Q_p(cfs)=640C_pA/t_l Where,
A=drainage area in square miles.
C_p=storage coefficient from 0.4 to 0.8, can be obtained from standard texts (inversely related to C_t).
The time base of the unit hydrograph is (days):
t_b=3 + (t_l/8),
Note:After plotting unit hydrograph, you should always check if the area under the unit hydrograph is 1.0 and the time base should be adjusted, if necessary, until the area under the unit hydrograph is 1.0.
The duration of excess rainfall, is (hr):
D = t_l/5.5.
If the unit hydrograph is desired for duration other than above, use following relation for adjusting lag time:
t_la=t_l+0.25(D_R-D)
Use this adjusted lag time in equation for computing peak flow, Q_p.
The other ordinates useful for shaping hydrograph are the widths at 50% and 75% of the peak flow values:
W₅₀=770(Q_p/A)^-1.08
W₇₅=440(Q_p/A)^-1.08

Following are the steps that you may find useful for constructing snyder UH:
1. Compute the lag time t_l for given C_t and C_p.
2. Compute the peak flow rate Q_p.
3. Find time base t_b. For small watersheds, time base can be estimated by multiplying time to the peak by 3 to 5.
4. Find duration of rainfall D.
5. Use W₅₀ and W₇₅ ordinates for shaping the hydrograph at 50% and 75% of the peak flows. W₅₀ and W₇₅ are located at 1/3 before Q_p and 2/3 after Q_p.
6. Ensure that the area under the constructed unit hydrograph is 1.0.