How to model waterflow when only a couple of sample points available

Figure below depicts a cross section of a creek for which I am trying to measure the water flow for that section. What we have as inputs are a bunch of sample points on the river. For each sample points we measured the depth of creek at that point (e.g. h1, etc) the velocity of water at that point(e.g. v1) and the distance of that sample point from the shore. For each area the water flow is defined as the multiplication of area times the velocity. Since we are given the h1,..hn and d1 ,.. dn we can easily measure each area thereby the water flow of that section.

areaFlow1 = [(v1+v2)/2][(h1+h2)/2][(d2-d1)]

However what I need to know here is how to aggregate all of those multiple area water flows to define the global water flow for that section?

Is it the best to say Global Water Flow ( for a cross section) = Sigma(areaFlow(1)..areaFlow(n))/ n ?

• Yes, if that's your estimate of the flux through one area, then the total flux is just the sum of the individual fluxes. This is a basic property of integration. I think a more interesting question is about the accuracy of your approximation for each area flux which is probably quite a poor estimate in most situations. – Doug Lipinski Apr 6 '14 at 19:33
• In your formula, you must not divide by $n$. The total water flow is simply the sum of the water flow through each of your sectors. – Wolfgang Bangerth Apr 7 '14 at 0:19