Fluid Mechanics problem: Oil pressure calculations in pipe flow

In summary: The viscosity is not relevant for the case with no flow, but it will be necessary for the case with flow. And yes, the incline is related to z1 and z2 as they represent the altitude differences between the two ends of the pipe. In summary, the problem involves an oil with density 900 kg/m3 and viscosity 0.18 Ns/m2 flowing through a circular pipe inclined at 40° to the horizontal. The length of the pipe is 10 m and the diameter is 6 cm. The fluid pressure at the lower end of the pipe is 350 kPa and the pressure at the upper end is 250 kPa. The relevant equations are the steady flow equation and the Bernoulli equation
  • #1
Motorbiker
32
1
Homework Statement
An oil with density 900 kg/m3 and viscosity 0.18 Ns/m2 flows through a circular pipe which inclines upwards
at 40° to the horizontal. The length of the pipe is 10 m and the diameter is 6 cm. The fluid pressure at the
lower end of the pipe is 350 kPa and the pressure at the upper end is 250 kPa. (i) Confirm that flow is upward
through the pipe
Relevant Equations
I think Steady flow equation
Problem Statement: An oil with density 900 kg/m3 and viscosity 0.18 Ns/m2 flows through a circular pipe which inclines upwards
at 40° to the horizontal. The length of the pipe is 10 m and the diameter is 6 cm. The fluid pressure at the
lower end of the pipe is 350 kPa and the pressure at the upper end is 250 kPa. (i) Confirm that flow is upward
through the pipe
Relevant Equations: I think Steady flow equation

I have been trying really hard to start this question, but I don't know what equations are relevant or how to start. I would be very grateful if someone could kindly explain the problem to me in basic terms. This way I will hopefully be able to attempt the question and post my attempt here if I need further help.

Thank you.
 
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  • #2
If the fluid were not flowing, what would the pressure at the top end be if the pressure at the lower end were 350 kPa?
 
  • #3
Chestermiller said:
If the fluid were not flowing, what would the pressure at the top end be if the pressure at the lower end were 350 kPa?

The pressure would still be 250kPa at the top end because pressure decreases with altitude.
 
  • #4
Oh yeah? OK, let's see your calculation to prove it.
 
  • #5
Chestermiller said:
Oh yeah? OK, let's see your calculation to prove it.

Am I correct in my understanding?

For the calculation, I will need to use the bernoulli's equation, is that right?
 
  • #6
Motorbiker said:
Am I correct in my understanding?

For the calculation, I will need to use the bernoulli's equation, is that right?
Your understanding was incorrect (quantitatively).

For the calculation without fluid flowing, the Bernoulli equation can be used.
 
  • #7
Chestermiller said:
Your understanding was incorrect (quantitatively).

For the calculation without fluid flowing, the Bernoulli equation can be used.

Thank you, can the sfee can be used instead?
 
  • #8
Motorbiker said:
Thank you, can the sfee can be used instead?
What is sfee?
 
  • #9
Chestermiller said:
What is sfee?
Ah sorry, I meant steady flow energy equation.
 
  • #10
Motorbiker said:
Ah sorry, I meant steady flow energy equation.
What does the steady flow energy equation reduce to if the flow is zero?
 
  • #11
Chestermiller said:
What does the steady flow energy equation reduce to if the flow is zero?
It reduces to zero?
 
  • #12
Motorbiker said:
It reduces to zero?
Let's stick with the Bernoulli equation (at least for now). So let's see your Bernoulli equation calculation.
 
  • #13
Chestermiller said:
Let's stick with the Bernoulli equation (at least for now). So let's see your Bernoulli equation calculation.
Sorry, I think misunderstood you. The steady flow energy equation should reduce to:

p1/pg + z1=p2/pg +z2+hf

I think this is correct for cases where the flow is zero.
 
  • #14
Motorbiker said:
Sorry, I think misunderstood you. The steady flow energy equation should reduce to:

p1/pg + z1=p2/pg +z2+hf

I think this is correct for cases where the flow is zero.
Well, hf is zero if there is no flow. Otherwise, OK.
 
  • #15
Chestermiller said:
Well, hf is zero if there is no flow. Otherwise, OK.

Okay great, I note that we have been given the viscosity in this problem, are we supposed to use it in this section?

Am I correct in thinking that the incline at 40 degrees is somehow related to z1 and z2?
 
Last edited:
  • #16
Motorbiker said:
Okay great, I note that we have been given the viscosity in this problem, are we supposed to use it in this section?9
if we are first doing the calculation for a case with no flow, why would we need the viscosity?
Am I correct in thinking that the incline at 40 degrees is somehow related to z1 and z2?
Correct.
 

Related to Fluid Mechanics problem: Oil pressure calculations in pipe flow

1. What is fluid mechanics?

Fluid mechanics is the study of how fluids, such as liquids and gases, behave when they are in motion or at rest. It involves understanding the forces and pressures that act on fluids, as well as the movement and behavior of fluids in different environments.

2. How is oil pressure calculated in pipe flow?

The pressure of oil in a pipe can be calculated using Bernoulli's equation, which states that the total energy of a fluid remains constant as it flows through a pipe. This equation takes into account the fluid's velocity, density, and height above a reference point, and can be used to calculate the pressure at any point in the pipe.

3. What factors affect oil pressure in pipe flow?

There are several factors that can affect the pressure of oil in pipe flow, including the fluid's viscosity, density, and velocity, as well as the pipe's diameter and length. Other factors such as changes in elevation and the presence of obstacles or bends in the pipe can also affect the pressure.

4. How does the viscosity of oil impact pipe flow?

The viscosity of oil, which is a measure of its resistance to flow, can greatly impact the pressure in pipe flow. Oils with higher viscosity will experience greater resistance and therefore require higher pressure to maintain a certain flow rate. This is important to consider when designing pipelines for oil transportation.

5. What are some real-world applications of fluid mechanics in the oil industry?

Fluid mechanics plays a crucial role in the oil industry, from the extraction and transportation of oil to its refining and distribution. It is used to design and optimize pipelines, pumps, and valves, as well as to understand the behavior of oil in different environments, such as deep-sea drilling or oil spills. It is also used in the development of new technologies for oil exploration and production.

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