# Cancelling out units in an equation

1. Apr 16, 2011

### andrewvidler

Hi i have done all the work for this problem calculating viscosity and i come to the last part where i need to manipulate and cancel out units to come to a final solution. The equation works out as

viscosity = 0.0042m^2 x 9.8m/s/s x 11,401.4kg/m^3 all divided by 1.034466m/s

viscosity is measured in Pascals/sec

can someone help me with the last step with the units

thanks

2. Apr 16, 2011

### CompuChip

I usually start by drawing a long horizontal line and writing all the units in the denominator or numerator as appropriate. Thereby, dividing by a/b means writing b "above" and a "below" (as dividing by a/b means multiplying by b/a).

In this case, going through them one by one, you'd get

$$\frac{m^2}{1} \times \frac{m}{s \times s} \times \frac{kg}{m^3} \times \frac{s}{m}$$
If you write this in a single fraction, and take the similar units together, you get
$$\frac{m^3 \, s \, kg}{s^2 \, m^4}$$
which is straightforward to simplify.

Now to check that this is indeed Pa/s, it is easiest to convert Pascals into kg/m/s. Personally, I find it easiest to remember that pressure is force per unit area, and Newton's law is F = ma, so
$$[Pa] = \frac{[F]}{[A]} = \frac{[m] [a]}{[A]} = \frac{kg \times m/s^2}{m^2} = \frac{kg \times m}{s^2 \times m^2}$$

3. Apr 16, 2011

### tiny-tim

welcome to pf!

hi andrew! welcome to pf!

(try using the X2 icon just above the Reply box )
nooo … viscosity is measured in Pascal.sec

4. Apr 16, 2011

### andrewvidler

thanks - my final units are 453 kg/sm. any chance on helping me how to get this into pascals which are measured in mPa s?

5. Apr 16, 2011

### tiny-tim

Pa.s = force.time/area = mass.time.acceleration/area

= mass.time.distance/time2.area