That was meant to be a tan. Thanks for pointing it out.

 

You're making your original mistake again with the areas. The important area is the area of the opening which is a constant, not the free surface area which varies with depth. Doubling the area of the opening doubles the volume taken in, and so the depth is multiplied by a factor of root 2 for the prismatic case and root 3 for the conic case.

 

The angle affects the scale, yes. It will still have a square/cube root relationship, but the coefficients will change.

I disagree.

With which part exactly?

My parameter statement is that height is fixed, H, regardless of our monkeying with slant angle. Given H, the scale stick is not dependent on the angle of the 'V'. Look in side view. We are equating the rectangle of rainfall RD to the area of the measurement triangle, and expressing everything in <h,H>.

 

Well I'll save time on the actual calculations, but the realtionship will be a cube root one.

Whenever I feel a faint fuzziness in understanding, I find paper.

I was taking the scale to be on the sloped side. You're right;)

Whoa, Mongoose, cool!!! Now please refer to my post in QUOTABLE QUOTES, the "Albers dictum" concerning the likelihood of communication! We have, temporarily broken the FLOW OF ENTROPY.

 

In the conical case there are two dimensions that slope. There is a [math]D^2[/math] on both sides of the equation, so again a vertical scale stick won't care. In my first 'V' case I had two vertical sides which I could mark, but in the cone either you include a center stick or consult with MrMongoose about a cosine relationship, yes.