What Equations to use for this Thermofluids Problem?

[Mason98]

Homework Statement

Homework help please, just need the equations to use

Relevant Equations

Unsure

Hi guys,
I have been searching the internet trying to find the right equations to use for this homework but i cannot find them :(.
I was wondering if someone could point me in the right direction and let me know which equations i need to use to work out my homework.
Any help would be appreciated. I am set different values for each (h,x,D,e/D,Q) etc.

So far I have worked out the length of the pipe by using Pythagoras theorem (600^2 + 2000^2 = sqrrt 2088). For Part B I have tried to use the formula Q = AV, Re-arranged to V = Q/A so i can find out the velocity. I have plugged in 0.01m^3/s / 0.3 m = 0.033 M/S^2 ?
I was then going to use the values i have from the equations to find reynolds number Re = ρVL / μ
p being = 1000kg/m^2 x (V) 0.033 x (L) 2088 / 0.0013.
To find the pipe friction factor i was going to divide 64/ reynolds number.
I'm not too sure quite confused will appreciate any help.

 

[Chestermiller]

Homework Statement:: Homework help please, just need the equations to use
Relevant Equations:: Unsure

Hi guys,
I have been searching the internet trying to find the right equations to use for this homework but i cannot find them :(.
I was wondering if someone could point me in the right direction and let me know which equations i need to use to work out my homework in (a,b,c,d).
Any help would be appreciated. I am set different values for each (h,x,D,e/D,Q) etc.
View attachment 259169

Cmon. You must have some idea how to do this. What are your thoughts so far? For part (a), what equation from HS geometry class can you use?

For part (b), what is the definition of the Reynolds number for pipe flow?

 

[Mason98]

I have edited in my steps i have done so far.
Thanks

 

[Chestermiller]

Homework Statement:: Homework help please, just need the equations to use
Relevant Equations:: Unsure

Hi guys,
I have been searching the internet trying to find the right equations to use for this homework but i cannot find them :(.
I was wondering if someone could point me in the right direction and let me know which equations i need to use to work out my homework.
Any help would be appreciated. I am set different values for each (h,x,D,e/D,Q) etc.

So far I have worked out the length of the pipe by using Pythagoras theorem (600^2 + 2000^2 = sqrrt 2088).

Where did these numbers come from? They don't seem to correspond to any of the cases in your table. Which case do you think you are considering? Plus,, please give the result for the square root.

For Part B I have tried to use the formula Q = AV, Re-arranged to V = Q/A so i can find out the velocity. I have plugged in 0.01m^3/s / 0.3 m = 0.033 M/S^2 ?

This is incorrect. What is the cross sectional area of the pipe? What is the correct velocity?

I was then going to use the values i have from the equations to find reynolds number Re = ρVL / μ
p being = 1000kg/m^2 x (V) 0.033 x (L) 2088 / 0.0013.

This is also done incorrectly. For pipe flow, the characteristic dimension is the diameter D of the pipe, not the length.

To find the pipe friction factor i was going to divide 64/ reynolds number.
I'm not too sure quite confused will appreciate any help.

If the flow is turbulent (based on the Reynolds number), then you should be using the Darcy-Weissbach correlation to get the friction factor. 64/Re applies only to laminar flow.

 

[Mason98]

Where did these numbers come from? They don't seem to correspond to any of the cases in your table. Which case do you think you are considering? Plus,, please give the result for the square root.

This is incorrect. What is the cross sectional area of the pipe? What is the correct velocity?

This is also done incorrectly. For pipe flow, the characteristic dimension is the diameter D of the pipe, not the length.

If the flow is turbulent (based on the Reynolds number), then you should be using the Darcy-Weissbach correlation to get the friction factor. 64/Re applies only to laminar flow.

Forget the table sorry these are my figures.• Height h: 600m

• Distance x: 2 km

• Pipe diameter D: 0.3m

• Pipe relative roughness ε/D: 0.002

• Volumetric flow rate Q: 0.01

• The pressure in the pipe just before it enters the reservoir, p2, is 3 bar.

• μ = 0.0013 kg/m.s

• ρ = 1000 kg/m3

for the pythagoras i did (h) 600^2 + (x) 2000^2 = 4360000. Square root of that is 2088m.

So to calculate the velocity of the water i need to do V = Q/A?
But to calculate A i need to use the pipe diameter and multiply by pi to get the cross sectional area?

 

[Chestermiller]

Look up the equation between the diameter and area of a circle.

 

[Mason98]

Hey I have calculated the water velocity to be V = Q/A A = 3.414 x 0.3 = 0.942 Q = 0.01 / 0.9424 = 0.0106 m/s.
I have then plugged this value into the reynolds equation: p (fluid density) = 1000kg ( velocity ) = 0.0106 Diameter = 0.3m . dynamic viscosity = μ = 0.0013

(1000 x 0.0106 x 0.3) / 0.0013 = 2446.1 so this is transient flow?
Thanks

 

[Chestermiller]

Hey I have calculated the water velocity to be V = Q/A A = 3.414 x 0.3 = 0.942 Q = 0.01 / 0.9424 = 0.0106 m/s.
I have then plugged this value into the reynolds equation: p (fluid density) = 1000kg ( velocity ) = 0.0106 Diameter = 0.3m . dynamic viscosity = μ = 0.0013

(1000 x 0.0106 x 0.3) / 0.0013 = 2446.1 so this is transient flow?
Thanks

The area of a circle is $\pi r^2$, with pi equal to 3.142

 

[Mason98]

okay so 3.142 x 0.15 ^ 2 = 0.0706 m/s
Then 1000 x 0.0706 x 0.3 / 0.0013 = 16312?
Thanks for replying i appreciate the help.

 

[Chestermiller]

okay so 3.142 x 0.15 ^ 2 = 0.0706 m/s

That is A in m^2, not v.

v = Q/A

 

[Mason98]

That is A in m^2, not v.

v = Q/A

Oh haha thank you :), so V = 0.01 / 0.0706 = 0.141643 m/s.

reynolds = 1000 x 0.141643 x 0.3 / 0.0013 = 32,686 ?

 

[Chestermiller]

Oh haha thank you :), so V = 0.01 / 0.0706 = 0.141643 m/s.

reynolds = 1000 x 0.141643 x 0.3 / 0.0013 = 32,686 ?

Good. Based on this value of the Reynolds number, is the flow laminar, or is it turbulent?

 

[Mason98]

Turbulent i believe, i'll have a look at the Darcy-Weissbach correlation to get the friction factor.
Thank you for ur help :)

 

[Mason98]

Good. Based on this value of the Reynolds number, is the flow laminar, or is it turbulent?

Hello,
I've managed to work out the friction using Darcy-Weissbach, how do i go about working out the pressure in p1? can i use p=pgh? or is it not that simple? not sure if i need to use Bernoulli equation or not. would appreciate any tips

 

[Chestermiller]

Hello,
I've managed to work out the friction using Darcy-Weissbach, how do i go about working out the pressure in p1? can i use p=pgh? or is it not that simple? not sure if i need to use Bernoulli equation or not. would appreciate any tips

Tip: Use the version of the Bernoulli equation that includes frictional drag term.