Solving Equations for undefined variable with units

You have a unit balance problem.

Mass flow (Q/h) needs to be mass/time, your equation gives mass only.

mass flow is density times area times velocity, so velocity is mass flow/(area x density).

But area (of a circle) is pi x r squared, not the fourth power.

Start there

Fred already commented on your unit problems, so I will deal with your Mathcad problems.

Get rid of the symbolic evaluation (right arrow) - you don't need it and it isn't aware of units.Treats them as unknown variables and so is not able to collect and simplify units.

When should I solve an equation symbolically and just numerically in terms of getting proper units?

Not solve, evaluate. And you don't need symbolic evaluation at all as you are doing just simple numeric calculations. If you don't like the units the normal numeric eval (=) yields, just overwrite the units with those you want and Mathcad will give you the correct value.

How should I declare variables that rely on other known and unknown variables?

known/defined variables: just use their name. You already did that

unknown variable you want to use late: you can't define a variable but must create a function.

Solve block: You probably used literature for Mathcad 15 (the better program anyway) or below. There is no "given" in Prime. Solve blocks are handled differently in Prime. You have to insert kind of an ugly template (ribbon Math, Solve Block), provide a guess value for the variable(s) to solve for and copy the equation(s) in this template. You may resize it but it still will look ugly.

See if the attached sheet helps but note that I haven't corrected your unit problem - I just added s^2 on the LHS so the units match and the solve block works.