Uniform Flow Computations

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Manning Roughness Coefficient

Uniform Flow Computations

The Manning’s formula and the continuity equation, Q = A V form the basic equations for uniform flow computations. The discharge Q is then given by :

\[Q = \frac{1}{n}A{R^{2/3}}\sqrt {{S_o}} \]

where :

Q : Discharge (flow rate) passing through the cross section

n : Manning roughness coefficient

A : Wetted area

R : Hydraulic Radius

So : Longitudinal bed slope

\[Q = K\sqrt {{S_o}} \]

where, K  is called the conveyance of the channel and expresses the discharge capacity of the channel per unit longitudinal slope.

\[K = \frac{1}{n}A{R^{2/3}}\]

Types of Problems for Uniform Flow Computations

Uniform flow computations problems are relatively simple. The available relations are :

The basic variables in uniform flow situations can be the discharge Q, velocity of flow V, normal depth yo, roughness coefficient n, channel longitudinal slope So and the geometric elements (bed width and side slope for a trapezoidal channel as an example). There can be many other derived variables accompanied by corresponding relationships. From among the above, the following five types of basic problems are recognized.

Problem Type 1

Given Data :

  • Normal depth yo
  • Manning roughness coefficient n
  • Longitudinal bed slope So
  • Cross section geometric data

Required : Discharge Q & Flow velocity V

Solution type : Explicit

Problem Type 2

Given Data :

  • Normal depth yo
  • Manning roughness coefficient n
  • Discharge Q
  • Cross section geometric data

Required : Longitudinal bed slope So

Solution type : Explicit

Problem Type 3

Given Data :

  • Normal depth yo
  • Longitudinal bed slope So
  • Discharge Q
  • Cross section geometric data

Required : Manning roughness coefficient n

Solution type : Explicit

Problem Type 4

Given Data :

  • Manning roughness coefficient n
  • Longitudinal bed slope So
  • Discharge Q
  • Cross section geometric data

Required : Normal depth yo

Solution type : Implicit

Problem Type 5

Given Data :

  • Manning roughness coefficient n
  • Longitudinal bed slope So
  • Discharge Q
  • Normal depth yo

Required : Cross section geometric data

Solution type : Implicit

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