As the cross-sectional area of a conduit decreases, the speed must increase in order to have the same flow rate. The ratio of the area and velocity must be the same in order to have the flow rate be the same through a conduit. This is referred to as the equation of continuity, which applies to any incompressible fluid.
BERNOULLI’S EQUATION So, when fluid flows into a channel that is narrower, its speed increases. This means that its kinetic energy increases. One has to wonder where this kinetic energy comes from as energy is neither created nor destroyed. This goes back to the idea that net work equals one-half mass times velocity squared minus one-half mass times the initial velocity squared. This is shown in figure 65:
Figure 65.
Net work done will increase the fluid’s kinetic energy. Remember, too, that the pressure equals area times force so that the pressure will drop in a rapidly-moving fluid. This explains why shower curtains bulge inward when the shower is on and running. In the same way, cars will experience a force toward a parallel-moving truck passing beside a car. This is because the high velocity of the truck will create negative pressure in the air (which is a fluid) around it. This leads to Bernoulli’s equation, which is the relationship between pressure and velocity in fluids. This is described in figure 66:
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