Horizontal open channel flow. Hydraulic jump calculation 1

[JochemGrietens]

Dear Fellow Engineers

I'm having an issues with my calculations. This case concerns a open channel flow that start off being supercritical on the left and turns into subcritical flow after a hydraulic jump.

Given:
Volume flow rate Q = 0.16m^3/s
Width of the channel b = 1m
Resulting fluidheight at the left h1 = +/-6cm.

The channel slope = 0. The channel is perfectly horizontal
Mannings coefficient : 0.012

Question : Distance from the left part untill the hydraulic jump occurs. L = ?

I integrated the backwater function:
i = 0 because of slope being zero

In the figure below the X axis denotes the distance from the left to the right of the channel. the Y-axis shows the height of the fluid height (purpl/pink curve). The blew curve is the conjugate height.

I know that L can be determined from this curve but i don't know how. Can someone halp out please ?

Thank you,
Jochem Grietens

 

[bimr]

There is no method to calculate L the way you have shown it. The "L" in your drawing shows some distance past the jump where the fluid has reached subcritical flow.

What you may calculate it the Length of the jump. L

See the method in the link:

http://www.tvrl.lth.se/fileadmin/tvrl/files/vvr090/lecture10_momentum_principle.pdf

http://www.google.com/url?sa=t&rct=...wFq0pBEx9A4dsV_SA&sig2=Fed9vtboULdurr3K8c4nxw

 

[JochemGrietens]

Hello bimr,

Thank you for the very usefull links u provided. I know that there is a way to calculate the length of the jump itself. But what i need is an estimation of the location of the start of the jump.

I have taken a look into the VBA Excell sheet (second link you provided). It depicts and calculates the distance "Lj". It's this value that i would like to be able to calculate. However, when i put my slope S0=0,it gives an error message saying that a devision by zero is taking place.

I find it hard to believe that there is no way to estimate Lj for horizontal channels.

Any input is very welcome.

Regards,
Jochem Grietens

 

[bimr]

You have a situation with different scenarios, a Gradually Varied Flow (GVF) section and a rapidly varied flow section hydraulic jump).

The GVF section is not a hydraulic jump, and is analyzed separately from the jump as per the attachment.

The hydraulic jump starts at y[sub]1T[/sub].

 

[JochemGrietens]

Bimr,

Thank you for that info. I am already aware of the different type of approximation GVF and RVF. But do you think it is possible to calculate a estimation of the end of the GVF zone. The pink curve in my original post was calculated using GVF assumptions and intigrating the backwater curve. However, i do not know where this GVF part wil switch into the hydraulic jump.

 

[bimr]

Where the GVF transitions to the hydraulic jump is called the point of inflection. Not aware of any method to calculate it. Would think if you have a critical application, it would be best to model it.

 

[cvg]

typical method is to solve the energy equation for cross sections along the channel, moving downstream using the standard step method. since your slope is flat, losses will consist of friction, contraction and expansion losses only. (most other losses are minor and can be ignored). this is an iterative procedure. a check should be made of the froude number at each section and once it approaches unity, flow will be critical and you can expect the hydraulic jump to begin. you can do similar starting from downstream hydraulic control, assuming subcritical flow and a standard step backwater analysis to determine where the jump ends. for the rapidly varying flow region you will need to use the momentum equation instead. The HEC-RAS reference manual describes this well.

 

[JochemGrietens]

Hi Cvg,

I have heard about this HEC-RAS software. Would this software be fit to simulate my case ?

I see there are many modules of the software. Which one would be fit for my case do you think ?

Regards,
Jochem

 

[cvg]

there is just one module and it is a free download. it would give a reasonable approximation for your channel.