Calculating Oil Flow Speed: Density 850 kgm^3, Pipe Diameter 8 cm

[ssb]

Homework Statement

oil w/ density of 850 kgm^3 goes through a pipe diameter 8 cm at a rate of 9.5 liters / s.
what is the speed of the oil?

Homework Equations

v_1 = (dv/dt)/a_1 = (9.5*10^-3)/(pi(.04)^2) = 1.9 m/s

The Attempt at a Solution

i have the solution because this problem was given to me. I just don't understand where the 10^-3 came from and how it was derived.

 

[hage567]

I just don't understand where the 10^-3 came from

It comes from converting the volume from litres into m^3.

 

[ogb p]

The 10^-3 is a conversion factor. Since the given flow rate is in liters per second, and the desired units for velocity are meters per second, we need to convert from liters to cubic meters. There are 1000 liters in a cubic meter, so we use the conversion factor 10^-3 to convert from liters to cubic meters. This is why the 10^-3 is used in the equation.