For steady flow, in other words, nothing is changing with time.

For steady flow, the mass is conserved.

So the mass flow rate, which is crossing section one upstream must be

exactly the same as the rate at which mass is passing downstream.

So therefore, m dot 1 = m dot 2 or

rho 1 A1V1 is rho 2 A2V2.

And for an incompressible flow, in other words, the density is constant,

which is the kind of fluid that we're most concerned with in this course,

then this reduced to A1V1=A2V2 or Q1=Q2.

In other words, the volumetric flow rate is constant or conserved in the pipe.

If the pipe is converging, like we've drawn in the diagram up at the top here.

In other words, A2 is less than A1, then V2 is greater than V1,

so the flow is accelerating.

Conversely, if the flow is diverging, in other words,

the cross-sectional area is increasing, then the flow is decelerating.

The velocity is decreasing.

If we have multiple inlets and outlets, for example, merging or

bifurcating flows, such as in this Y shape branch here,

then the appropriate equation is that the summation of the mass flow

out is the equal to the summation of all of the mass flow rates in or

summation in rho Q is equal summation out rho Q.

And again, for an incompressible flow, the density is constant and cancels out.

Leaves us with the sum of the volume flow rates in is equal to

the sum of the volume flow rates out.

So in this example, what's entering in here m dot 1 = m dot 2 + m dot 3.

Or for an incompressible fluid, Q1=Q2+Q3.

Now let's do some simple examples and

we're given that the water is flowing through the converging pipe as shown.

If the water is incompressible, the velocity is decelerating,

accelerating, constant or cannot tell?