Piping Pressure Drop

A handy relationship for turbulent flow in commercial steel pipes is:

DP_F = W^1.8µ^0.2/20.000d^4.8r

where:

DPF	=	Frictional pressure loss, psi/lOO equivalent ft of Pipe
W	=	Flow rate, lb/hr
µ	=	Viscosity, cp
r	=	Density, lb/ft³
d	=	Internal pipe diameter, in.

This relationship holds for a Reynolds number range of 2,100 to 10⁶. For smooth tubes (assumed for heat exchanger tubeside pressure drop calculations), a constant of 23,000 should be used instead of 20,000.

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Source : Branan, Carl R. "Estimating Pressure Drop," Clzenzicnl Engineel-irzg, August 28. 1978.

Velocity Head

Two of the most useful and basic equations are

Dh = u²/(2g)
DP(V) + Du²/(2g) + DZ + E = 0

where :

Dh	=	Head loss in feet of flowing fluid
u	=	Velocity in ft/sec
g	=	32.2 ft/sec2
P	=	Pressure, lb/ft2
V	=	Specific volume, ft3/lb
Z	=	Elevation, feet
E	=	Head loss due to friction in feet of flowing fluid

In Equation 1 Dh is called the “velocity head.” This expression has a wide range of utility not appreciated by many. It is used “as is” for

1. Sizing the holes in a sparger
2. Calculating leakage through a small hole
3. Sizing a restriction orifice
4. Calculating the flow with a pitot tube

With a coefficient it is used for

1. Orifice calculations
2. Relating fitting losses, etc.

For a sparger consisting of a large pipe having small holes drilled along its length Equation 1 applies directly. This is because the hole diameter and the length of fluid travel passing through the hole are similar dimensions. An orifice on the other hand needs a coefficient in Equation 1 because hole diameter is a much larger dimension than length of travel (say ¹/₈ in. for many orifices).

For compressible fluids one must be careful that when sonic or “choking” velocity is reached, further decreases in downstream pressure do not produce additional flow. This occurs at an upstream to downstream absolute pressure ratio of about 2 : 1. Critical flow due to sonic velocity has practically no application to liquids. The speed of sound in liquids is very high.

Still more mileage can be gotten out of Dh = u²/2g when using it with Equation 2, which is the famous Bernoulli equation. The terms are

1. The PV change
2. The kinetic energy change or “velocity head”
3. The elevation change
4. The friction loss

These contribute to the flowing head loss in a pipe. However, there are many situations where by chance, or on purpose, u²/2g head is converted to PV or vice versa.

We purposely change u2/2g to PV gradually in the following situations:

1. Entering phase separator drums to cut down turbulence and promote separation
2. Entering vacuum condensers to cut down pressure drop

We build up PV and convert it in a controlled manner to u²/2g in a form of tank blender.

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Source :
Branan, C. R. The Process Engineer’s Pocket Handbook, Vol. 1, Gulf Publishing Co., Houston, Texas, p. 1, 1976.

A Mistake in Kern's Heat Transfer

Chemical engineers must be familiar with this set of equations, for designing a shell & tube heat exchanger.
The third equation for F_T then plotted in some figures, corresponded to type of shell & tube exchanger flow. for example in the figure below. This set can be found in any reference that talk about shell & tube heat exchanger, and I think all of that refer to the main source, Kern's "Heat Transfer".

Let's check these cases out...

< case 1 >A stream 90 °C is going to be cooled to 70 °C using cold stream 30 °C, which its temperature will rise to 50 °C. We'll find, the value of R will be 1. Use this value in the equation for F_T & LMTD. The value will be indefinite. So we cannot calculate the first equation.
< MyOpinion >The temperature differences are equal in both sides (T1-t2 = T2-t1), thus we can assume that the weighted/average temperature difference in this system is the same of those temperature differences, so we could use one of those. We can replace the F_T.LMTD in the first equation with TD, which TD=T1-t2=T2-t1. We can see the similar condition in the system which use latent heat in both streams.

< case 2 >A stream 90 °C is going to be cooled to 60 °C using cold stream 30 °C, which its temperature will rise to 70 °C. In this system, we can calculate the value of LMTD, but not for the F_T (it will be indefinite), so we cannot calculate the first equation for Q.
< MyOpinion >Examine the system, we will find that there will be cross temperature difference there. So, we cannot apply the combination of parallel-countercurrent (1-2, 1-4, 1-6, 1-8) to this system. We must use the fully countercurrent (with 1-1 exchanger) to this system, and replace the F_T.LMTD with LMTD only, in the first equation.

Those are my opinions. I hope there will be other opinions, or comments. I'm affraid, perhaps i missunderstood the problem, then please send comment, or tell me the truth....thanks :)