# Fully developed flow, Reynolds number

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1. Apr 13, 2015

### rustyrockets

Hi,
For my experiment I was asked to determine the length of the tube for a fully developed flow to occur ( Entrance length as shown in the attachment) , with the following flow parameters.
Flow rate : 1, 5, 15 lit/min
Fluid: Water
Tube Id: 1 inch.
My question How do I find out the length of the tube required to have a fully developed flow at its end. A valve is connected to the end, so the flow should be fully developed at the end when it hits the valve. The length of the tube is unknown. How would one use reynolds number to calculate this when I have both the length and the reynolds number not known.

Thanks & Regards

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Last edited: Apr 13, 2015
2. Apr 13, 2015

### Staff: Mentor

Bird, Stewart, and Lightfoot, Transport Phenomena give an equation for estimating the hydrodynamic entrance length for laminar flow in a tube.

Chet

3. Apr 14, 2015

### rustyrockets

I did not understand it, can you please explain

4. Apr 14, 2015

### Staff: Mentor

Which part don't you understand? What was the equation they presented for calculating the entrance length?

Chet

5. Apr 14, 2015

### rustyrockets

I was asked to calculate the entrance length,
I have the parameters flow rate 1,5,15 lit/min
Hydraulic diameter 1inch
fluid: water
density of water 1000kg/m3
Absolute (dynamic) viscosity - μ - Ns/m2 = 0.000404
hydraulic diameter 1 inch=0.0254meters
using the equation Le/D= 0.06Re , Le/D= 4.4(Re)^(1/6)
I calculated the values and got them as 3.1m, 0.5m, 0.6m respectively for their flowrates. Do you think this is correct?

6. Apr 14, 2015

### Staff: Mentor

Well now, this is more like it! I'm assuming that you did the arithmetic correctly. What were the values of the Re's that you obtained in each case, and which equation did you use in each case.

Chet

7. Apr 14, 2015

### rustyrockets

8. Apr 14, 2015

### Staff: Mentor

9. Apr 14, 2015

### rustyrockets

I was worried , if i made any conversion mistakes or any other arithmetic mistakes with formula i used.

10. Apr 14, 2015

### Staff: Mentor

Well, since you used online software to do the calculations, it's hard to imagine how that would be possible. I urge you to do the calculations without resorting to the online software, to develop your skill at converting units.

Chet

11. Apr 14, 2015

### rustyrockets

I have one more questiion, Im also using a mixture of Glycerol and water in ration of 40:60, I calculated the reynolds number for the similar flowrates and foound them to be 254,1268,3804 respectively

3804 is transient flow, how do i calculate the Le for that?

12. Apr 14, 2015

### Staff: Mentor

Calculate it from both equations, and use whichever is larger.

13. Apr 14, 2015

### rustyrockets

sounds perfect, thank you :)

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