How to calculate n with its uncertainty in the equation Q= kL(h^n)?

[Joon]

Homework Statement

I was given a flow rate equation Q= kL(h^n), where k is a constant and L (width of rectangular weir) was set to 0.625 ft. A table of experimental Q values and corresponding h' and h values was provided, please refer to the picture attached. h (weir head) in the equation= h in the table. h= h' -0.3290 ft.

There are two variables in the equation, Q and h, and I need to determine the experimental value of n.

An example calculation was provided where the used equation was D=cE^n and I was told to use the same method as the one used in the example calculation. Please refer to the attached files 2-4 for the example calculation.
I get how to calculate the uncertainty of D, but I really have no idea how the uncertainty of E was calculated.
After calculating U(D) and U(E), a plot of ln (D) against ln (E) was drawn to calculate n (the gradient of the graph).

Could someone help me understand this?

Relevant Equations

Q= kL(h^n) for the task

D=cE^n for the example calculation

Hook gauge reading, weir head- vernier scale
Flow rate Q reading- venturi flow meter

I am thinking of doing the same thing (summing up all the uncertainties that contribute to U(E) in the example) for the task, so summing up all the fractional uncertainties that contribute to U(Q). But the problem is unlike energy in the example, I'm not sure what's the contributors that lead to U(Q).

 

[BvU]

I must be missing something: in the example I don't see a calculation of $n$ at all, only a (remarkable coincident) result for $g$ ?

 

[Joon]

The process is a bit complicated, I am uploading everything I have, please have a look.
I'm attaching the excel file as well where the example calculation was done.

 

[Joon]

2 more files