Pressure drop in fluid flowing between flat plates 1

[GeorgeEllwood]

Hello,
I was wondering if anyone can help. I'm looking for a formula to estimate the pressure drop in a fluid as it flows in the gap between two flat parallel plates.
I'm using a formula to calculate the velocity of a fluid as it flows between two parallel plates. This needs to know the change in pressure over distance, dP/dx.
At the start of the gap there is a 1 bar driving pressure. I've assumed that the pressure drop is 1 bar divided by the distance the fluid has travelled.
However this doesn't seem to agree with some CFX modelling and some experimental results.
Is there a better approximation for the pressure drop?
Thanks
George

 

[ione]

Look for Darcy Weisbach equation:

deltaP = f*L*rho*V^2/(Dh*2)

being in your specific case the hydraulic diameter Dh = 2d (where d is distance between parallel plates)

 

[waterpipe]

Well, you have not mentioned what is your case and its applicability. The friction factor is much dependent on the distance of plates from each other which dictates the flow condition. This is a classic example in most Fluid Dynamic books (such as Nakayama).
you might find these links helpful:

http://www.coolingzone.com/library.php?read=489

&

http://www.electronics-cooling.com/2003/05/estimating-parallel-plate-fin-heat-sink-pressure-drop/

 

[GeorgeEllwood]

Hello,
Thanks for the replies. I'm trying to model the flow of a viscous (10 Pa.s) epoxy resin flowing between two parallel plates, under atmospheric pressure, i.e. the two plates are in a vacuum tank and outside the vacuum tank the resin is admitted through a feed through. This provides almost 1 bar of pressure to push the resin through the parallel plates. I'm using this formula to calculate the fluid velocity.

velocity = 1/(2*viscosity) * (dP/dx)*(y^2-h^2)

where x is the distance travelled
h is the half gap between the plates

I've been assuming that the dP/dx term is given by the driving pressure (~1 bar) divided by the distance the resin has travelled. This doesnt' agree with some CFD modelling carried out on the problem. The CFD modelling is ~25% faster than the text book solution.
I've tried to include Darcy Weisbach equation as suggested but I've got something wrong somewhere and it's making the resin speed up over time not slow down.
The gap is 1mm and the plates are ~300mm wide and 800mm long, the viscosity is 10Pa.s and the pressure is ~1 bar, the flow is laminar.
I'm hoping to benchmark the CFD modelling against the text book answer or find a reason why they're out by ~25%.
Many thanks
George

 

[BigInch]

Not sure, but isn't epoxy resin a non-Newtonian fluid?

Only put off until tomorrow what you are willing to die having left undone. - Pablo Picasso

 

[GeorgeEllwood]

It is but in this case I'm treating it as a Newtonian fluid. I'm trying to get my CFD model using a Newtonian fluid to agree with a text book case also using a Newtonian fluid before I go any further.
Thanks
George

 

[btrueblood]

Is your CFD model using a laminar viscosity model? It probably should be given the description, though we are still lacking knowledge of the actual gap between the plates.

 

[GeorgeEllwood]

Hi btrueblood, the gap is 1mm.

 

[BigInch]

What physical significance are you using for y in y^2-h^2

The equation says that when y=h, velocity is 0.
Isn't the y term describing the y value in an (x,y) cartesian flow field and h (parallel to y) is relating the head at that point (over x) to dP across the total length of the field.

In that case, when y = h you have no flow, where in the hydraulic system you describe, velocity would be maximum midway between the two plates.

You seem to be using a groundwater flow through a porous medium equation to describe flow between plates, if I'm not wrong.



Only put off until tomorrow what you are willing to die having left undone. - Pablo Picasso