# Intro to Continuity Now that the 'basics' are out of the way, let's look at something more difficult. However, there are a couple extra conditions we have to apply to this fluid before we can truly dive into things, namely: 1. The fluid **must not be viscous** - meaning it must flow with no internal impediment Viscosity is the **fluid's resistance against flowing**, like how glue takes much longer to flow a certain distance than water! 2. The fluid **must undergo laminar flow** - meaning it flows in one direction without fail, so no turbulence! This also means the volume of fluid travelling through a certain area must be equal at all times. 3. The fluid **must not be flowing in rotation**. That means it can't This gives us an *ideal fluid* - where the pain of university-level fluid dynamics can be completely sidestepped. Sometimes, pressing the tap down creates jets of water that seem to travel much, much faster than if the tap were left by itself. Why is that? Note that this means the speed of the water therefore depends on the cross-sectional area it flows through. Since the fluid is incompressible, the volume of the water flowing out of the tube won't change. Let's express this volume $V$ in terms of its speed $v$ and area $A$. The regular time interval $t$ can be defined in order to standardise this: $V = vA t$ Since rate of volume is conserved another expression can be used to express it: $A_{1}v_{1} = A_{2}v_{2}$ This relation is known as the "**Equation of Continuity**" - which we can also express as a rate equation: $R = Av$ Note that this is the rate of flow for the volume. The mass rate of flow can therefore be given as the density times the volume, as shown: $R_{M} = \rho Av$ %%diagrams for laminar flow%% # Extending the Equation of Continuity # What's Next?