# Flow and Viscosity

1. Mar 24, 2016

### cjm181

1. The problem statement, all variables and given/known data

For many liquids the viscosity is strongly dependent on temperature. Use the table below to estimate the required maximum temperature of crude oil to flow at a rate of 4Kg s-1 through a 0.3 metre diameter pipe whilst maintaining a laminar flow.

In the table it has in the rows.

temp 0 20 50 100 200
Viscosity 16 7.5 4 2.5 1.5

Crude Oil (sg = 0.885)
Viscosity (x10-3 Nsm-2)

2. Relevant equations
A=PIr^2

V=m/(PA)

Viscosity=(Pvd)/Re

3. The attempt at a solution

Area of pipe = PIr^2=PI*0.15^2=0.07069m^2

V=m/(pA)
V=4/(855*0.07069)
V=0.066m/s

So for the pipe of diameter 0.3m, to achieve 4kg/s we need a fluid velocity of 0.066m/s. (sounds really slow?)

Then
Reynolds # = (density)(velocity)(pipe diameter) / (viscosity)

Viscosity=(density)(velocity)(pipe diameter) / (reynolds)

so if the flow is to be laminar, set reynolds no to 1999

Viscosity=(855)(0.066)(0.3) / (1999)

Viscosity=0.00849 or 8.49x10^-3Nsm

so max temp would be around 16deg C. Can anyone confirm?

Kr
Craig

2. Mar 24, 2016

### Staff: Mentor

Confirmed. Btw, you don't need to know the specific gravity to solve this.

3. Mar 25, 2016

### cjm181

Thanks Ches

Can you show me how to do it without SG?

Kr
Craig

4. Mar 25, 2016

### Staff: Mentor

$$Re=\frac{\rho vD}{\mu}=\rho v \left(\frac{\pi D^2}{4}\right)\frac{4}{\pi D\mu}=\frac{4\dot{m}}{\pi D\mu}$$

5. Oct 27, 2016

### DC83

hi, I'm a new member, I was just hoping someone could explain why 855 has been used in some equations and why it isn't 0.855. Thanks

6. Oct 27, 2016

### Staff: Mentor

HI DC83. Welcome to Physics Forums.

0.855 is the specific gravity, which is the density relative to water. The density of water is 1000 kg/m^3. So the density of the oil is 855 kg/m^3.

7. Jun 10, 2017

### jaff90110

Hi
I'm just wondering from the post 1 said
Where do we get that Temperature from ? Is that came from the table or something ? as I have not got a clue.

8. Jun 10, 2017

### Staff: Mentor

9. Jun 10, 2017

### jaff90110

I'm sorry , that was my mistake,
From the post # 1 that said the max temperature is around 16 degree C.
I'm wondering that where did cjm181 get that temperature from?

10. Jun 11, 2017

### Staff: Mentor

He calculated the Reynolds number at the different temperatures based on the viscosities in the table, and then interpolated to find the temperature at which the Reynolds number exceeds 2100. Use semi-log paper to plot the viscosity as a function of temperature. Please show your graph.