The first thing to do when calculating any kind of fluid flow is to apply conservation of mass.
In this case a mass flow rate equation can be applied.
The mass within a set space at any given time can be represented by M. To determine how mass changes with time we take the derivative and get dM/dt. As mass flows through a certain volume it is a function of the volume flow rate and the density of the fluid. This can be represented by dM/dt = Rho x Q where Rho is the density of the fluid and Q is the volume flow rate of the fluid. This can be further simplified to dM/dt = Rho x V x A where V is the linear velocity of a flow and A is the cross sectional area through which the flow is moving.
Now depending on whether you are talking about an air intake system on something going fairly slow, or something in the compressible flow regime you’d have some different courses of action.
I’ll assume you’re talking about the intake on the combustion engine of a car. Incompressible flow is probably a good assumption in this regime.
In incompressible flow the mass of a system does not increase so dM/dt = 0. This can be written as dMin/dt – dMout/dt = 0 or dMin/dt = dMout/dt. Where dMin/dt is the rate at which mass is entering the system and dMout/dt is the rate at which mass is leaving the system. This equation can then be written as :
Rho Vin Ain = Rho Vout Aout
If you assume a constant density you get Vin Ain = Vout Aout. The velocity of the fluid at the entrance and exit of a system is inversely proportional to the ratio of entrance and exit areas. This will help when it comes to changing diameters in a pipe, like in an intake system.
Bernoulli’s equation can help us get a little further. It relates density and velocity to pressures in a flow.
Bernoulli’s equation for incompressible flows is:
(V^2)/2 + gz + p/Rho = C
Where C is a constant. In this case the effects of gravity on the flow is negligible so we can omit the gz term. This equation means that anywhere in the flow of an incompressible fluid the addition of these terms will remain constant.
By multiplying through by Rho we get:
½ Rho V^2 + p = C1
Where C1 is also constant since density is assumed constant. ½ Rho V^2 is what is commonly referred to as dynamic pressure while p is what is commonly referred to as static pressure. C1 in this case can be replaced with a total pressure Po which is the sum of the static and dynamic pressure. Dynamic pressure can be thought of as the pressure a moving flow would have at a location where the flow stops. Anyway, in the case of your intake system ½ Rho V^2 + p = Po, where Po is the total pressure of the flow.
Now is where it gets a little more specific to the type of intake you’re trying to calculate the pressure loss for. If you’re using a ram air intake your calculation will depend on the flow speed of the air entering the intake. Po will be ½ Rho V1^2 + p1 where ½ Rho V1^2 is the dynamic pressure of the flow of air outside of the intake and p1 is the external static pressure. Po is also equal to ½ Rho V2^2 + p2 where ½ Rho V2^2 is the dynamic pressure of flow inside your intake system and p2 is the static pressure of the flow inside your intake system.
So: ½ Rho V2^2 + p2 = ½ Rho V1^2 + p1
If you don’t have a ram air style intake you can neglect the external dynamic pressure as V1 goes to zero.
You’re going to need to find a way to either measure or calculate the mass flow rate of your engine at any given moment to find the pressures you’re looking for. To calculate, it will depend on the displacement of your engine, whether it’s 2 or 4 stroke, the RPM’s, and quite possibly the orientation of the cylinders. This equation gives the theoretical volume flow rate in CFM:
Q = (ED x RPM x VE)/(ES x C)
Where Q is the volume flow rate, ED is the engine displacement in cubic inches, RPM is the current RPM of the engine, VE is volumetric efficiency, a good guess for this would be roughly 75%, ES is the stroke of your car’s engine 2 for a four stroke, and 1 for a 2 stroke, C is a conversion factor from cubic inches to cubic feet which is equal to 1728.
It may be more accurate to measure it. Most mass flow sensors can be read with a special program on a laptop, or simply a volt meter (provided you have the conversion factor).
Once you have the volume flow rate, you can calculate the velocity from the area of your intake opening. Q/A = V
Plug your velocities, densities, and pressures into the Bernoulli equation and you should have a pressure for inside your intake now.
All of this so far could be done with a pressure sensor, but if you don’t have the equipment, this should provide a good estimate for intake pressure at the entrance of the intake pipe.
Pressure loss can be estimated through a pipe but largely depends on whether there is turbulent or laminar flow in the pipe. Some pressure loss will occur due to friction and turbulence, as well as bends in the pipe. There are some good online calculators for HVAC systems such as Pressure-Drop. You will need the volume or mass flow rate and kinematic viscocity (which can be looked up easily) to calculate. Some calculations also require a pipe roughness factor which is provided in a table at Pressure-Drop.
Another good resource for calculating pressure drop is this site:
http://knol.google.com/k/how-to-calculate-pressure-drop-and-friction-losses-in-a-pipe#
Again, much of this depends on whether your flow is laminar or turbulent, which can be estimated using the Reynold’s number. Re = (V x d)/Mu where V is the velocity of the flow, d is the diameter of the pipe, and Mu is the kinematic viscosity.
If Re is less than 2500 it is probably Laminar, if it is over 4000 it is probably turbulent.
You can calculate head loss fairly easily using the formulas at that site.
In an intake system you’re looking at moving air through a filter, a tube or airbox of some kind, a mass airflow sensor (MAF), then the intake manifold where the air will pass through valves into the engine cylinders. On most fuel injected engines there is also a manifold absolute pressure (MAP) sensor in the intake manifold. If you can read this pressure you can find the drop in pressure from the intake entrance pressure you calculated earlier.
In a turbo or supercharged system the air will move through a compressor and intercooler, where the intake air is cooled and compressed, before getting to the intake manifold.
Every bend and length of tube will cause some pressure loss. An optimized system will try to maintain laminar flow throughout the system to reduce losses. The best way to do this is to have a short, smooth, wide pipe with few bends and a high flow filter. Some systems use flow screens to prevent turbulence as well. A system with a compressor overcomes these losses by increasing the pressure by using some of the engine’s power. However, optimization allows an even better increase in pressure.
Any specific questions just ask. ; )
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