That makes sense, thank you. I'm guessing then that since only a relatively minor fraction of fluid molecules are impacted by protuberances and their impacts are at lower velocity, the effects are negligible for laminar flow.
Hi,
I've been reading over Transport Phenomena by Bird, Stewart, and Lightfoot and I've been going over the friction factor ##f##. I've gone through the whole development leading to the observation that, for time-averaged turbulent flow, when we neglect entry effects, ##f = f(Re; k/D)##, where...
Hey, thank you for taking the time to write that.
So, for the stress vector exerted by the fluid immediately below the plane at y on the fluid immediately above the plane, the normal vector is now ##\vec{i_y}##, so:
$$\vec{t} = \vec{\Pi}\centerdot \vec{i_y} = P\vec{i_y} + \tau_{xy}\vec{i_x} =...
Well, if I'm not misunderstanding you, I don't think my confusion really stems from misunderstanding tensors - I'm still just struggling to see why the tensors point in the directions they do in some situations. I don't know if there's been a misunderstanding, so I just want to reiterate what's...
Sorry about that, I originally meant to write:
\frac{τ_{yx}}{dy} = -\frac{dp}{dx}
I just realized I changed my mind or something when I wrote the equation in my other post and the accompanying paragraph didn't make sense. That must have been really confusing, even I can't really see what I...
Well, for the case of parallel infinite plates, I arrived to:
\frac {dv_x}{dy} = -\frac{1}{μ} \frac {dP}{dx}
This can be integrated twice and the constants of integration can be found by the no-slip condition at the top and bottom plates. I might be making a mistake, but I'm not getting that...
Hi guys,
I've been working through some notes on Transport Phenomena by Bird and I've basically been just developing velocity and shear stress profiles for various (simple) models by a differential momentum balance and I'm trying to understand why a certain result happens.
When looking at...
Well, my goal is pretty much getting from
\frac{T_2 - T_1}{T_3 - T_2}
to
\frac{(V_1/V_2) - 1}{(P_2/P_1) - 1}
Applying ideal gas law would make my expression in terms of different Δ(PV). I'm not sure if there's something obvious with the algebra I'm missing. I'm not really seeing how I...
Homework Statement
A possible ideal-gas cycle operates as follows:
(i) from an initial state (p1,V1), the gas is cooled at constant pressure to (p1,V2)
(ii) the gas is heated at constant volume to (p2,V2)
(iii) the gas expands adiabatically back to (p1,V1).
Assuming constant heat capacities...
Ohhh, I was looking at it completely wrong. I was misinterpreting where the last equation was coming from. What you're saying makes much more sense. Thanks a lot, much appreciated!
I'm not really understanding why they cancel. The only thing I can see being canceled in steady state considerations are time-dependent factors, which neither S or T1 is.
I'm going through the solution to a problem that was assigned to my class and there's a step I don't really understand which I think is a concept I'm misunderstanding.
1. Homework Statement
The curved surface of a cylinder of radius R and length L is insulated. The face at x = L is maintained...
I got about 6.408 x 10^-9 J. If the number sounds wrong, I calculated total energy E from
E^2 = p^2c^2 + (mc^2)^2
Then I used the relationship between total energy, rest energy, and kinetic energy to find kinetic energy.
K = E - mc^2
Hey Orodruin, you're right, I had completely forgotten about
E^2 = p^2c^2 + E_0^2
I guess since I've only recently learned it, it's not sticking out to me in my mind compared to other more grounded ideas. I guess the electron's speed is just nearly c and my calculator's just showing me c...
Homework Statement
What is the kinetic energy of an electron with a momentum of 40 GeV/c?
The Attempt at a Solution
Kinetic energy involves velocity of the particle so my first thought was to write momentum in terms of velocity.
p = \frac{mv}{(1-(v/c)^2)^{1/2}}
p^2 = \frac{(mv)^2}{(1 -...