Calculating Air Intake Pressure: A Beginner's Guide

[Max_VQ]

(First post!)

The other day I was using my OBD-2 scanner and found out that my car's intake has a peek flow of 25 lbs/min. I converted this to ~317 cubic feet (at 5.5 deg C)

I then calculated the velocity in the 3.5" diameter intake to be ~36 feet/sec.
The intake has a 2" venturi orifice (sound muffler) and calculated the flow at this point to be ~64 feet/sec.

Here is where I am stuck. How do I calculate the pressure difference?

Thank you in advance!

 

[FredGarvin]

To accurately calculate the expected delta P you need to have the venturi's discharge coefficient. The coefficient is a function of the geometry and is calculated during tests. Venturis usually have pretty high Cv values when compared to an orifice (usually close to 1) but they do vary with Reynolds number.

The standard calculation for flow through a venturi device is

$$Q = C_v A_t \sqrt{\frac{2 \Delta P}{\rho(1-\beta^4)}}$$

Where:
$$Q$$ = Volumetric flow rate
$$C_v$$ = Discharge coefficient
$$A_t$$ = Throat area
$$\Delta P$$ = Pressure difference
$$\rho$$ = Flowing density
$$\beta$$ = Diameter ratio

 

[stewartcs]

I think the standard Cv is taken as 0.975 but varies with the Reynolds number.

 

[stewartcs]

Just to add my 2 cents...since this is compressible flow, you'll probably need to include a gas expansion factor in Fred's equation. Although, if the delta P is less than 10% (if memeory serves me correctly), Crane TP410 say's that you can use incompressible flow as an approximation. So you'll probably be ok with the first equation.

 

[Max_VQ]

The standard calculation for flow through a venturi device is

$$Q = C_v A_t \sqrt{\frac{2 \Delta P}{\rho(1-\beta^4)}}$$

Where:
$$Q$$ = Volumetric flow rate
$$C_v$$ = Discharge coefficient
$$A_t$$ = Throat area
$$\Delta P$$ = Pressure difference
$$\rho$$ = Flowing density
$$\beta$$ = Diameter ratio

Wow! Thanks for the quick replies.

Are my units correct:
$$Q$$ = Volumetric flow rate in CFM
$$C_v$$ = Discharge coefficient
$$A_t$$ = Throat area in inches squared
$$\Delta P$$ = Pressure difference in inches of water??
$$\rho$$ = Flowing density in pounds/min
$$\beta$$ = Diameter ratio 3.5:2