Transport Processes problem regarding viscosity/fluid flow and energy.

[nefizseal]

Hey guys, there is this superhard question (atleast for me). I've been trying at it for days but I seem to get nowhere.


The Trans-Alaska Pipeline System (TAPS) carries around 100,000m³ of oil per day from the Northern Alaskan oil fields to the nearest ice-free port of Valdez, around 1300km away. The pipe has an outer diameter of 1.22m and a wall thickness of 12mm. Eleven pumping stations are used along the total length of the pipeline to transport the oil.

Note: Assume that the pumping stations are equally spaced along the pipeline, that the pipe is roughly straight and horizontal, and that the flow with the pipe is laminar, Newtonian and steady-state. Also assume that the pumps are 100% efficient so that all energy consumed by the pumps is dissipated by the fluid. The density and kinematic viscosity of the oil are (rho)=890 kg/m³ and (nu)= 7.17 x 10^-4 m² /s respectively.


(a) Starting from first principles, estimate the pressure increase that must be generated by each of the eleven pumping stations to maintain the flow.


(b) The rate that energy is dissipated D(W) by a fluid when it flows through a horizontal pipe under the influence of a pressure difference is given by

D = (delta)P x Q

where (delta)P is the difference in pressure between the inlet and outlet to the pipe (Pa), and Q is the volumetric flowrate through the pipe (m³/s). How much power (rate of energy use) is required to maintain the flowrate of oil through the entire pipeline?

If oil is burned to power the pumps, and 3.6 x 10⁴ MJ of energy can be harnessed from burning 1 m³ of oil, what percentage of the total flowrate needs to be burnt to maintain the flow?

 

[nefizseal]

Well here is what I have done so far (which isn't much to be honest)


I know that the density is 890 kg/m³ and I also know that the kinametic viscosity is 1.17 x 10^-4 m²/s


I know from basic principles that kinametic visc. = viscosity/ density

So I can get, absolute viscosity = density x kinametic visc.

So my absolute viscocity comes to 0.638 Pa s = (mu)


I don't exactly know what to do from here. I mean, they said how much pressure do I need to maintain flow. But then there are 11 pumps, do I divide something by 11 1st and then get it and what do I do? Will I need the measurements of the pipe for it?

I don't really want the answer as much as I would want someone to tell me what to do?

And I am completely clueless about the 2nd part...I mean I can solve the whole differential equation thing to get Vx, Vmax, Q etc. for a general flow in a cylindrical pipe, but I don't know what exactly I should do...

Thanks

 

[nefizseal]

Actually, I got the answer to the first part. It was pretty easy. Just had to solve the equation for the Horizontal pipe. Can someone help me with part B? COME ON MAN!

 

[abc007]

Given :
Q = 100,000 m3/day * 1 day/24 h * 1 h/60 s = 69.444 m3/s
OD = 1.22 m , ID = 1.196 m , Lt = 1300 000 m , Laminar flow
L = 1300 000 m/11 = 118182 m
µ = 0.638 Pa.s , ρ =890 Kg/m3


Starting from first principles, estimate the pressure increase that must be generated by each of the eleven pumping stations to maintain the flow.

from Hagen-Poiseuille Law can be rephrased as :
Q = π*ID4*(-ΔP)/(8*µ*L)
-ΔP = 8*Q*µ*L/ (π*ID4)
 ΔP = 8*69.444*0.638*118182/(3.14*1.196^4) = 6519921.438 Pa = 65.2 bar

The rate that energy is dissipated D(W) by a fluid when it flows through a horizontal pipe under the influence of a pressure difference is given by
D = (delta)P x Q
D= 6519921.438 * 69.444 = 452.769424 MW

How much power (rate of energy use) is required to maintain the flowrate of oil through the entire pipeline?

power for pump = Q*ΔP
since we have 11 pumps then
Total Power = 11* 6519921.438 * 69.444 = 4980.4637 MW

If oil is burned to power the pumps, and 3.6 x 104 MJ of energy can be harnessed from burning 1 m3 of oil, what percentage of the total flowrate needs to be burnt to maintain the flow?

(4980.4637 M J/s needed)/(3.6 x 10^4 MJ/m^3 provided) ==0.1383 m^3/s

so 0.1383 m3/s of oil have to be burn to provide enough energy for pumps.

% of flow needed to be burned = 0.1383/69.444 *100 = 0.199 %

Please let me know If you find that my answer is wrong .

 

[alphy]

I would approach this problem by first understanding the basic principles of fluid flow and energy. Viscosity is a measure of a fluid's resistance to flow, and in this case, the kinematic viscosity of the oil is given as 7.17 x 10-4 m2/s. This value, along with the density of the oil, can be used to determine the dynamic viscosity, which is a measure of the internal friction of the fluid.

To estimate the pressure increase required by each pumping station, we can use the Bernoulli's equation, which states that the total energy of a fluid remains constant along a streamline. This means that the energy gained by the fluid due to the pumping stations must be equal to the energy lost due to frictional losses in the pipe.

Using this equation, we can calculate the pressure increase required at each pumping station by dividing the total energy gained by the volumetric flowrate through the pipe. This will give us an estimate of the pressure difference that must be generated by each pumping station to maintain the flow.

To determine the power required to maintain the flowrate through the entire pipeline, we can use the given formula D = (delta)P x Q, where D is the rate of energy dissipation, (delta)P is the pressure difference, and Q is the volumetric flowrate. This will give us the power required to maintain the flow in watts.

Finally, we can use the given information about the energy harnessed from burning 1 m3 of oil to determine the percentage of the total flowrate that needs to be burnt to maintain the flow. This can be calculated by dividing the power required by the energy harnessed from burning 1 m3 of oil and then multiplying by 100.

In conclusion, solving this problem requires a thorough understanding of the principles of fluid flow and energy, as well as the ability to apply these principles to real-world scenarios. It is a challenging problem, but with the right approach and calculations, a solution can be reached.