Kinetic Energy

[DummyCivilEng]

In the CERM Chapter 16 (Fluid Flow Parameters):

In Section 14, it says that for laminar flow, kinetic energy is

E_v = v_ave^2

whereas in Section 2, it says that kinetic energy is

E_v = v^2/2

Can anyone explain why the factor 2 is missing? What is the relationship between v of Section 2 and v_ave. I don't think v is v is v_max?

Thanks,

Dummy

 

[John QPE]

I'm in the 10th Edition, and in Flow Parameters it has EV=(v^2/2)

My section 2 is Engineering Drawing, so I'm not too sure what you are looking at there.

 

[ptatohed]

In the CERM Chapter 16 (Fluid Flow Parameters):

In Section 14, it says that for laminar flow, kinetic energy is

E_v = v_ave^2

whereas in Section 2, it says that kinetic energy is

E_v = v^2/2

Can anyone explain why the factor 2 is missing? What is the relationship between v of Section 2 and v_ave. I don't think v is v is v_max?

Thanks,

Dummy

I believe the first equation you list (Ev = vav2 [Eqn 16.32 in CERM 13, SI units] ) is for laminar flow and the second equation you list (Ev = v2/2 [Eqn 16.3 in CERM 13, SI Units] ) is for uniform/turbulent flow. Does that help?

 

[DummyCivilEng]

I'm using CERM 14th Edition.

The formula Ev = v2/2 shown in Section 2 is general; it does not refer to uniform, turbulent, or any type/regime of flow. (I think the terms "uniform" and "turbulent" are supposed to mean two different things). Also, if you read carefully in that section is says that v is "average velocity"
.

In the CERM Chapter 16 (Fluid Flow Parameters):

In Section 14, it says that for laminar flow, kinetic energy is

E_v = v_ave^2

whereas in Section 2, it says that kinetic energy is

E_v = v^2/2

Can anyone explain why the factor 2 is missing? What is the relationship between v of Section 2 and v_ave. I don't think v is v is v_max?

Thanks,

Dummy

I believe the first equation you list (Ev = vav2 [Eqn 16.32 in CERM 13, SI units] ) is for laminar flow and the second equation you list (Ev = v2/2 [Eqn 16.3 in CERM 13, SI Units] ) is for uniform/turbulent flow. Does that help?

 

[matt267 PE]

I think (and hopefully someone will correct me if I'm wrong), section 2 gives you the kinetic energy for a fluid flow of uniform velocity (turbulent flow). Where as section 14 talks about laminar flow where the velocity is 0 at the pipe walls and maximum at the center (see Figure 16.3 in the 13th edition). Because the flow profile for laminar flow is parabolic, the kinetic energy is found by integrating equation 16.30 (13th edition).

In truly turbulent flow, the velocity is the velocity. As shown in figure 16.3, the velocity is the same across the pipes cross section. With laminar flow, you're going to have a max velocity and an average velocity because the flow is not equal across the pipes cross section. Again, see figure 16.3.

Hopefully I got that right. It's the theory I'm taking with me in October.

 

[DummyCivilEng]

Hi matt267,

It seems you are correct:

http://www-mdp.eng.cam.ac.uk/web/library/enginfo/aerothermal_dvd_only/aero/fprops/cvanalysis/node41.html

Thanks,

Dummy

I think (and hopefully someone will correct me if I'm wrong), section 2 gives you the kinetic energy for a fluid flow of uniform velocity (turbulent flow). Where as section 14 talks about laminar flow where the velocity is 0 at the pipe walls and maximum at the center (see Figure 16.3 in the 13th edition). Because the flow profile for laminar flow is parabolic, the kinetic energy is found by integrating equation 16.30 (13th edition).

In truly turbulent flow, the velocity is the velocity. As shown in figure 16.3, the velocity is the same across the pipes cross section. With laminar flow, you're going to have a max velocity and an average velocity because the flow is not equal across the pipes cross section. Again, see figure 16.3.

Hopefully I got that right. It's the theory I'm taking with me in October.