# Continuity

The dynamics of flowing fluids is more difficult than statics, but this is good news. It means the MCAT will test only some of the basic principles.

The first principle is continuity. Figure 10-10 shows a river, in which point 1 is in a slow, lazy flow, while point 2 is in the rapids. Why does the water flow faster at point 2? During one second the number of gallons flowing past point 1 is the same as the number flowing past point 2. (Think about it. If the water level between 1 and 2 is constant, then the inflow must equal the outflow.) The difference is that point 2 has a smaller cross-sectional area.

The rate at which a fluid passes by a point, measured in volume per time, is called the flow rate f. In a steady state, the flow rate is the same at each point along the flow:

Figure 10-10

 f1 = f2 ...(12)

Now we can relate the flow rate to the actual speed of the fluid. Think of water going through a garden hose. If we turn up the faucet, then the flow rate and the flow velocity both increase. We can also obtain a greater flow rate by increasing the cross-sectional area. We would guess (correctly) that we could write

 f = Av. ...(13)

The discussion in this section refers to any incompressible fluid, that is, liquids. It also applies to compressible fluids, like air, if the fluids are not, in fact, compressed.