 So we just derived the continuity equation. Now what we're going to do in this segment is going to look at a few simplifications of the continuity equation. So I'm writing up the continuity equation in differential form. That's what it'll look like. Simplifications that we can sometimes come across. First of all we could be dealing with flow fields that are steady. So if we have a steady flow then the partial by partial t term would be equal to zero and what we then end up with is just del dot rho v equals zero. If we have an incompressible flow we know for incompressible density is equal to a constant. If density is equal to a constant the time rate of change of density will be zero. So what we then end up with is del dot v equals zero and del dot v remember when we looked at the vector operators we said that that was the divergence operator and that's quite often whenever you talk about an incompressible flow you always say del dot v is equal to zero but expanding that out what it looks like is the following. So that would be for an incompressible flow. Now in the case of liquids, liquids for the most part in fluid mechanics we view as being incompressible and in the cases of gases they're incompressible for velocities less than a Mach number of 0.3 and Mach number is defined as the local flow speed divided by the speed of sound. So m is the Mach number and a here would be speed of sound. So as long as we stay at 30 percent or lower than the speed of sound in air then for the most part we can view the flow as being incompressible and then we can simplify the continuity equation in the way that we've just seen. So the main one is whatever you're dealing with incompressible flows you all often hear people say del dot v is zero and that is then just a shorthand notation for the continuity equation for an incompressible flow field. What we'll do next we'll look at a different coordinate system for the continuity equation. We're going to look at the cylindrical coordinate system and then we'll solve the problem and then after that we'll move on to momentum.