Fluid mechanics help!

[ConceptuallyInept]

One would assume that when the area of an orifice is doubled then twice as much water will flow through this orifice. Hence we assume a proportional relationship between the two. However use of a garden hose leads us to believe that increasing the area of the orifice decreases the velocity of the water hence implying an inverse relationship.

I need a theoretical relationship between the diameter of a circular orifice and the flow rate of water discharged from this orifice.

Your help would be greatly appreciated

[HallsofIvy]

I don't see the "however". If, indeed, twice as much water flowed through twice the area, that would imply that the velocity of the water stays the same! What are you assuming is constant? The pressure on the water?