Question

The Muskingum model of routing a flood through a stream reach is expressed as O₂ = K₀I₂ + K₁I₁ + K₂O₁, where K₀, K₁ and K₂ are the routing coefficients for the concerned reach, I₁ and I₂ are the inflows to the reach, and O₁ and O₂ are the outflows from the reach corresponding to time steps 1 and 2 respectively. The sum of K_O, K₁ and K₂ of the model is
1. -1
2. -0.5
3. 0.5
4. 1

Answer 1

Correct Answer - Option 4 : 1

Concept:

A common method of Hydrologic channel routing is Muskingum method, in which the channel storage in a reach is expressed as a function of both inflow and outflow discharge.

S = k [x Im – (1 - x)Qm]

Where, s = Storage in a channel reach

I = Inflow Discharge

Q = Outflow Discharge

k → Coefficient known as storage time coefficient. It was unit of time, it is approx. equal to time of travel of flood wave through the channel reach.
x → Weightage factor. Its range series from 0 to 0.5

• For naturally occurring channels m = 1, Hence the equation becomes

S = k [x I – (1 - x)Q]

• For x = 0, storage is only a function of outflow discharge. Such reservoirs are also known as Linear Reservoir.

Muskingum model of routing a flood through a stream reach is expressed as

O₂ = K₀I₂ + K₁I₁ + K₂O₁

where K₀, K₁and K₂ = Routing coefficients for the concerned reach

I₁ and I₂ = Inflows to the reach 1 and 2

O₁ and O₂ = Outflows from the reach 1 and 2

K₀ + K₁ + K₂ = 1.0