Pressure drop per unit length of the pipe

[umalik]

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Viscous liquid (ρ = 1460 kg/m3, μ = 5.2×10−1Ns/m2) is pumped through a smooth pipe with a 0.1 m diameter, at a rate of 5×10−2m3/s. Using your Fanning friction factor versus Reynolds Number plot to estimate the driving force needed to maintain the flow rate mentioned earlier. I need to express the driving force in terms of pressure drop per unit length of the pipe. No length is provided so the force will be a function of pressure drop and a constant of L.

I've found the the velocity, reynolds number. The fanning friction factor I got was by reading of the subsequent friction factor for the calculated reynolds number from the plot. I'm not sure where to go from here as I've used the darcy-weisbach pressure loss equation but don't know to solve the equation with varying units. Could someone guide me as to what to whether I've taken the correct approach and how I should go about solving the equation?

Thank you so very much.

 

[Chestermiller]

Have you calculated the shear stress at the wall, τ? How is the pressure gradient in the tube related to the shear stress at the wall?

Chet

 

[umalik]

Have you calculated the shear stress at the wall, τ? How is the pressure gradient in the tube related to the shear stress at the wall?

Chet

Thank you for your reply. I'm not sure how the shear stress can be calculated without the length for the pipe.
I've calculated an answer of approximately 1629 N/m from the pressure loss equation. Not sure if that is correct.

 

[Chestermiller]

Thank you for your reply. I'm not sure how the shear stress can be calculated without the length for the pipe.
I've calculated an answer of approximately 1629 N/m from the pressure loss equation. Not sure if that is correct.

I'm not going to check your result, but have you ever seen the following equation?
$$\tau = \frac{1}{2}\rho v^2 f$$
where f is the friction factor and τ is the shear stress at the wall.
Have you ever seen the following equation?
$$Δp=4\frac{L}{D}τ$$
What does that tell you about Δp/L?

Chet

 

[umalik]

Ahhh, great. Thank you so much. Could I just ask, as to when the darcy-weisbach pressure loss equation is used? What are the specific conditions for using that to calculate pressure drop rather than the pressure gradient method that you mentioned? I'm unable to find any specific information in the textbooks I have.

 

[Chestermiller]

It's really the same thing. The Darcy friction factor is 4x the Fanning friction factor that I used.

Also, in flow in a pipe, the pressure gradient is constant, so
$$\Delta p=\frac{dP}{dx}L$$
Chet

 

[yuchen]

Ahhh, great. Thank you so much. Could I just ask, as to when the darcy-weisbach pressure loss equation is used? What are the specific conditions for using that to calculate pressure drop rather than the pressure gradient method that you mentioned? I'm unable to find any specific information in the textbooks I have.

i am doing this question, too. how did you solve it finally? i don't understand what does it mean by driving force in terms of pressure drop per unit length, does that ask us to express the function in terms of pressure drop and L? or do you actually solve it...