Unit Conversion: Solving for Speed of Water Flow

[smray7]

Homework Statement

water flows into a tube with a diameter of 6.35 cm at 0.012 meters cubed per sec.
it exits the nozzle with a diameter of 2.2cm at what speed?

Homework Equations

a = pi r squared

A1V1 = A2V2

The Attempt at a Solution

My question is should i convert the cm to meters?
how do you know when to do unit conversions?

 

[danago]

Homework Statement

water flows into a tube with a diameter of 6.35 cm at 0.012 meters cubed per sec.
it exits the nozzle with a diameter of 2.2cm at what speed?

Homework Equations

a = pi r squared

A1V1 = A2V2

The Attempt at a Solution

My question is should i convert the cm to meters?
how do you know when to do unit conversions?

In this case it will not matter. In general, an equation is only correct if the units are the same on both sides of the equality sign.

If you use area A1 in cm² and velocity in m/s, the left hand side will have units of cm² m/s. This will be equivalent to the right hand side if you also use cm² for A2.

Another way to think about it is if you rearrange the continuity equation you get:

$$\frac{A_1}{A_2} = \frac{V_2}{V_1}$$

i.e. the ratio of outlet velocity to inlet velocity is equal to the ratio of inlet area to outlet area. Since we are talking about a ratio of areas, it really does not matter what the units are, as long as they are the same.

 

[smray7]

ok thanks, that's clears things a little. on another problem i have to determine the pressure on wing two.

airplane mass: 1.60 x 10^4
wing one area : 40m^2
wing two area : 40m^2
pressure on wing one : 7.00 x 10^4
pressure on wing 2: ?

F= PA
mg = P1A1 + P2A2
mg = A(P1 + P2)

mg -P1
_______ = P2
A


so anyhow i have some number and the unit as:

(#kg)(#m/s) - (#Pa)
_______________
#meters squared

i know pressure is measured in Pascals, but when all is said and done, none of the units cancel. does that matter?

 

[noleguy33]

Recheck your algebra and your unit for g... the units work out fine.

You will get X pascals = P2

 

[rwisz]

As a scientist, it is important to pay attention to units in any calculation or problem. In this case, since the given diameter is in centimeters, it would be helpful to convert it to meters to maintain consistency in units. This will also make it easier to use the equation A1V1 = A2V2, where A represents the cross-sectional area and V represents the velocity. In general, it is important to do unit conversions when the given data or equation requires it, or when it helps to simplify the problem. It is always a good practice to double check units and make sure they are consistent throughout the problem.