Maximum Flow Rate in Open-Channel Flow for a Circular Pipe - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Applications and Example Worksheets : Science and Engineering : Maximum Flow Rate in Open-Channel Flow for a Circular Pipe

Maximum Flow Rate in Open-Channel Flow for a Circular Pipe

Introduction

This application determines the greatest attainable water flow rate in a partially filled circular pipe.

 

 

It uses the Manning formula to determine the flow rate in the open-channel flow of water:

where:

 

• 

Q is the flow rate

• 

n is an empirical coefficient

• 

A is the cross-sectional area of flow

• 

R is the hydraulic radius

• 

S0 is the incline of the channel

 

An equation that represents the hydraulic radius of a partially filled circular pipe is derived and substituted into the Manning formula. The resulting equation is then optimized to find the maximum flow rate.

 

Manning Formula for a Circular Pipe

 

Manning formula:

 

For a partially filled circular pipe, the flow area (the blue shaded area in the preceding diagram) is:


The wetted perimeter is given by the following formula.

 

Hence, the hydraulic radius, R, is:

(2.1)

The Manning formula then becomes:

(2.2)

Maximum Flow Rate for a Circular Pipe

Pipe radius:

Incline of the channel:

Roughness coefficient:

 

(1)

The maximum flow rate is...

(2)

...when  is ...  

(3)

... and the flow depth is:

(4)

 


Download Help Document