Calculating Velocity in a Venturi Effect Nozzle: Converting Units

[ISX]

Homework Statement

Venturi effect nozzle.. Starts off at 100cm and goes down to 40cm. The flow rate of the gas is 2.23 m3/s. What is the average velocity at the beginning and end of the nozzle.

Homework Equations

Continuity Formula, Bernelli = Q = A1V1=A2V2

The Attempt at a Solution

It's not the solution I am having trouble with so much, I am having a brain fart with units. I can take the area of 100cm and get 7850 cm2 and 40cm works out to 1256cm2 and you end up with a starting velocity of 0.000284 and an ending velocity of 0.001775 which I am assuming is cm/s.. Is that right or do I need to convert 100cm and 40cm to meters first and then do the calculation and then end up with meters/s?

 

[TSny]

I can take the area of 100cm and get 7850 cm2 and 40cm works out to 1256cm2 and you end up with a starting velocity of 0.000284 and an ending velocity of 0.001775 which I am assuming is cm/s.

Hi ISX. No need to assume anything here. If you carry your units along in the calculation it will guide you. You have V = Q/A. You plugged in numbers as V = (2.23 m³/s)/(7850 cm²). So, what do the units reduce to here?

 

[ISX]

I guess I've never read it like you put it, just always had a guide to follow in the book. I see cubic meters and cm squared so I woulda thought you would make them both cm or both meters..so I'm still not sure.

 

[TSny]

I see cubic meters and cm squared so I woulda thought you would make them both cm or both meters..so I'm still not sure.

Right. You can go either way: convert the cm² to m² or convert the m³ to cm³.

 

[ISX]

Alright so both of these should be right then.

 

[TSny]

Yes. Nice.

 

[ISX]

Schweeeeet. Thanks.