Use find to solve a iteration

You have three equations, but only one variable to look for. This usually can't work.

One option is to turn the first two equations into functions of h_n -> A(h_n):=... and U(H_n):=....

You should put these two function definitions in front of the solve block as well as the definition of the variables I_S, Q and k_St.

In the solve block a guess value for h_n is missing! You may use h_n := 1m

At the end remove the square brackets around h_n. Simply write h_n := find(h_n)

As you are just looking for one variable another option is to use the "root" function in one of its two flavors instead of the solve block with "find".

Here is a way how to do it. For convenience reasons I defined a function "flowrate" but you could use the expression directly in the root command as well.

BTW, a third option which I won't recommend is to use the solve block with all three equations as you had them setup.

Move the three variable definition outside the solve block and above it.

Provide guess values for all three variables hn, A and U at the top of the solve block and at the end let the Prime look for all three variables by writing

BTW, a function "flowrate" might also be useful to demonstrate the behaviour of the flowrate with respect to the value of hn

Important! For future question always attach the worksheet itself, not just a picture which does not even show which error message you get (presumably "variable not defined").

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@SO_10687563 wrote:
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Once I find the hn that gives me the correct flow rate Q, I can always scale it afterwards, like double hn to get b and turn it back into a rectangle if needed.

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Not sure how you would do so!??

In case you think that you only have to keep the area constant (double hn and use hn/2 for b) this would be wrong as the flowrate seems not only be dependent on the cross-sectional area.

The relationship between h and b is shown here

The green trace is the correct one and its based on an equation of fifth order.

The blue trace only lets the cross sectional area constant (so we see a simple hyperbola), but because the circumference is changing, flowrate will not be kept constant that way.

To give a numeric example. If you double hn -> h=63.238 cm, the correct value for b would be b=18.746 cm. If you simply keep the area constant, you would end up with just 15.81 cm!

The highlighted function shows how you could get the b-value for any given value of h using the "root" function.
Of course you also use "root" with a guess value or a parametrized solve block function as shown in Terry's first reply.

And sure you can also modify it to let you calculate the correct h-value for any given b.

Check the function for the flow rate! I have no experience in your field of work and only guessed from your initial posting ...

Terry has done a good job of pointing out that you need to learn how to use Mathcad.

But if I look at your picture:

Your equation doesn't balance.

And if I web search "Strickler coefficient," I can quickly find a wikipedia page, https://en.wikipedia.org/wiki/Manning_formula#Hydraulic_radius that shows this problem's math.  There are two quantities that you need to address: a hydraulic radius, and the hydraulic gradient.  (The hydraulic radius allows you to develop the "non-square" channel.)

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