Advanced /Surface Hydrology Dr. Jagadish Torlapati Fall 2017 MODULE 2 - ROUTING METHODS

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1 Routing MODULE - ROUTING METHODS Routing is the process of find the distribution of flow rate and depth in space and time along a river or storm sewer. Routing is also called Flow routing or flood routing. Two different types of routing models Hydraulic routing Hydrologic routing Hydrologlic Routing Involves the simultaneous solution of continuous equation and a storage volume equation written as a function of inflow and outflow flowrates. The basic equation used in hydrologic routing is called the continuity equation. ds = I(t) O(t) dt This is often applied to storage reservoirs and storm-water detention basins. Two types of methods are used: Modified Puls method (storage is a function of outflow rate, for example: storage basin) Muskingum Method (Storage is a function of both inflow and outflow, for example: channel routing) Modified Puls method Over a finite time interval between t and t+dt, the continuity equation can be written as: S S 1 = I + I 1 Δt O + O 1 Rewriting the above equation for convenience ( ) + S 1 I 1 + I Δt O 1 = S Δt + O The subscripts 1 and refer to the values at times t and t+dt. What are the known and unknown parameters in the above equation? All inflows are known (usually inflow hydrographs are given) For any reservoir, we can figure out the storage vs stage (Z) relationship Also outflow for given stage can be determined by equations. Steps involved to route the inflow hydrograph through a reservoir 1

2 S 1 1. Substitute the known values of I 1, I and Δt O 1. This gives the values of S Δt + O. From the reservoir and outlet structure characteristics, determine the discharge, O S corresponding to the calculated value of Δt + O. S 3. Subtract O from Δt + O S 1 to yield Δt O 1 at the end of this time step. 4. Repeat the steps 1 to 3 until the entire outflow hydrograph is calculated. Problem 1 A stormwater-detention basin is estimated to the have the following storage characteristics Stage (m) Storage (m 3 ) The discharge weir from the detention basin has a crest elevation of 5.5m and the weir discharge is given by Q=1.83H 5/ The catchment runoff hydrograph is given by Time (min) Runoff (m 3 /s)

3 ELEVATION-STORAGE-DISCHARGE RELATIONSHIP Stage (m) Storage (m 3 )

4 Time (min) Runoff (m 3 /s)

5 Muskingum method Developed for Muskingum river basin in eastern Ohio by McCarthy in It is primarily used for routing water in drainage channels including rivers and streams. The routing expression for this method is given as: where C 1, C and C 3 are given by O j+1 = C 1 I j+1 + C I j + C 3 O j Δt KX C 1 = K(1 X) + Δt Δt + KX C = K(1 X) + Δt K(1 X) Δt C 3 = K(1 X) + Δt It should be apparent that C 1 +C +C 3 =1 The time step should be taken such that it lies between KX and K(1-X) to ensure that you do not get negative flows. A convenient value for time step can be between K/3 and K. Problem The flow hydrograph at a channel section is given by Time (min) Runoff (m 3 /s) Time (min) Runoff (m 3 /s) Use the Muskingum routing method to estimate the hydrograph 100 m downstream from the channel section. Assume that X=0. and K=40 minutes. 5

6 Time (min) Runoff (m 3 /s) Outflow (m 3 /s)

7 Problem 3 The flow hydrograph at a channel section is given below. Use Muskingum routing to find the outflow. The Muskingum parameters are as follows: X=0.15, K =.3 minutes Time (hr) I (m 3 /s) Outflow (O) (m 3 /s)

8 Problem 4 The flow hydrograph at a channel section is given below. Use Muskingum routing to find the outflow. The Muskingum parameters are as follows: X=0.3, K = 35 minutes Time (hr) I (m 3 /s)