How to solve this flow rate system using the solve block (iteratively)

[AB_10071877]

Hi, we are working on a project and we can not figure out why our solve block is having errors. We are looking to optimize the flow rate, but we need to find all the friction factors and Reynolds numbers, and pressure changes in each pipe. We are using the Chen equation, which includes flow rate and Reynolds number. Please help! Also, any other tips would be greatly appreciated!!

[LucMeekes]

Expressed assuch in the Solve block, there's little for Prime to solve. Your DeltaP.1 is defined above the solve block to be calculated by the DeltaP function, using the value of Q.1 that is unknown at that time (of definition). Hence DeltaP.1 (and all the other DeltaP.x) are unknown inside the solve block. There's no way for Prime to know that you mean DeltaP.1 to be dependent on Q.1.

Solution:

Instead of DeltaP.1, put in a call to the function DeltaP(Q.1,...) in the equation inside the solve block. And of course the same for all the other DeltaP.x.

Then you have 16 equations, so you can solve for 16 unknowns (at maximum, assuming that the equations are independent), I'd guess you want to solve Q.1 through Q.16, not just Q.1 alone.

There's no point in setting (guessing) Re.1. The DeltaP function doesn't need them. Once you have the Qs you can calculate your 16 Re.x numbers with the Re() function.

Success!

Luc

[ValeryOchkov]

See please chapters 16 and 17 here

Thermal Engineering Studies with Excel, Mathcad and Internet | Valery Ochkov | Springer

[Sergey]

A very nice reference. Thank you for sharing

[terryhendicott]

Hi,

The first and second equations for change of pressure in the solve block have all positive pressure values summing to zero.  This is impossible arithmetically so some of the flows must have negative pressure?  This means negative flows in opposite direction from that assumed.

The equation for change of pressure has Q squared which always returns a positive pressure.  I have included the sign function so it is possible to get negative pressure from a negative flow regime.   Hence the first and second pressure change equations in the solve block can have sums that sum to zero.

Enclosed is file with solution.

[AB_10071877]

Unfortunately, I can't open it because our school uses MathCAD 4.0 Prime. It won't let me open it. Could you provide more screenshots of possible?

[LucMeekes]

"our school uses MathCAD 4.0 Prime" Then Why was your original file a Prime 6 file...?

Anyway, here's Terry's file in Prime 4.

Success!
Luc