Practical Process Engineering

This relation is derived from mass/ momentum/energy balances for isentropic flow of ideal gas

It shows clearly for a given change in gas velocity (dV/V; V: Velocity), the resulting change in density will also depends on the square of the Mach number. For example, at Mach number 0.1, the fractional change in density will be 1% (0.01) of the fractional change in velocity. Similarly, at M=0.33, it will be about 10% of this fractional change of velocity. Therefore, at low Mach numbers, the density changes will be insignificant but as it increases, the density changes sibnificantly and, thus, compressibility effects will become increasingly important.

Bernouli and darcy-weisbach equations are deveoped to calculate velocity-pressure relation mainly for compressible (i.e. liquids) fluids. The main assumption is incomressibility of liquids: their density is almost constant. However, accepting such assumption for gasses results in wrong calculation, because gases are compressible and their volume/ density may be changed largly under common industrial processes. While there are various equations and emprical relations for gas flow, only two above mentioned equations control liquid hydraulics. So, it would be a great victory if we find a way to use these well-understood equations for gases. The key is desnsity; if it doesn't change greatly, incompressibility assumption works for gases. Here, we are looking for conditions under them the gas density is almost constant or the amount of error resulting from incompressibility assumption is somehow we engineers are happy with that. Before taking the further step, let's talk about some basics of incompressible gasses. ***Mach Number: Continuty equation or conservation of mass : d( Instead of using reynolds number to catagorize flow regimies, Mach number is employed to recognize the type of flow: M= u/C u is the gas local velocity and C is the sound velocity in the medium. C= squart( gamma* Z* R* T/ M.W); gamma= Cp/Cv Z= compresibility factor R= universal gas constant T=absolute temperature M.W= Molecular weight Incomressible flow regimies are catagorized as below: 1- Subsonic flow for M<1 2- Supersonic flow M>1 3- Transonic flow between subsonic and supersonic flows 4- Hypersonic flow for M»1 (even greater than 5) The simplest case is isentropic (adiabatic+ reversible) flow of ideal gas. Combining momentum and mass balances gives us below equation:

#Compresssible_Fluids #Bernouli_Equation #Darcy_Weisbach_Equation Incompressible fluid equations like bernouli and darcy-weisbach are well understood for decades, while compressible fluid relations have always some degree of uncertenity. When "incompressiblity assumpltion" is applicable to compressible fluids? How serious is the error? This is our today topic.

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Send me the solution for question number 6.

Recommended pressure drop is 0.1 bar for 50 m. So for 30 m, it is 0.06 bar roughly. If the second formula is used to calculate pressure drop: For D=200 mm —---> Delta P= 0.08 For D=250 mm —---> Delta P= 0.02 'd' is right answer.

Solution to question 5) L=30 m P= 10 barg —---> Specific Volume(Vg)= 0.1772 m^3/Kg m (flowrate)= 20000 Kg/h As mentioned earlier, saturated steam velocity should be between 25-40 m/s. For this range, the minimum diameter should be 200mm. See marked up nomogram👇🏼👇🏼👇🏼

Solution to question number 4) There are two general rules for saturated steam: 1- Velocity should be between 25-40 m/s to minimize errosion. For long runs or torturous lines, lower velocity should be chosen to lower the pressure drop. 2- Pressure drop should not exceed 0.1 bar per 50 m. You can use both nomograph and table to find suitable pipe diameter for 4 barg saturated steam. Both 80 mm and 100 mm are good, but the line is torturous and pressure drop should be checked. Without doubt, a line with greater diameter can lower the pressure drop. As we do not know the velocity, 100 mm pipe is the reasonable choice even it is a little bit costy. So, part 'a' is right answer.

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