I had a spare moment at work so I looked up jet boats in Mark's Standard Handbook for Mechanical Engineers. The thrust is m dot *(Vjet - Vboat). This is derived from impulse-momentum which is a sort of rearrangement of the common formula from Sir Isaac,
F = m * a to: f = m * dV/dT to: f dT = m * dV from which: f = m/dT * dV or: f = m dot * change in velocity In air, the force would be just m dot * V because the total change in velocity is V because the water comes to rest. In the case of a boat, the change in velocity may not be so high because the boat actually may be moving! 8-) So now we just need to know what the final velocity of the water in the bucket is as well as the m dot I mentioned the other day. The m dot is easy because that's the fill rate. I would say that at this point, one goes empirical and just measures stuff. Obviously the water flow in the bucket may resemble the exterior of a torus and so one measures the velocity of the water near the hose but upstream of its exit to get the equivalent of Vboat. I can't remember what the other sundial-related stuff is just now. John B
