# Pipe in network

1. Mar 11, 2016

### foo9008

1. The problem statement, all variables and given/known data
in the second picture (refer to the circled part) , i can understand the ΣKQ^n , but i dont understand the second one , why it will become ΔQΣKnQ^(n-1) ?

2. Relevant equations

3. The attempt at a solution

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2. Mar 11, 2016

### BvU

Can't read the exponents. Did you understand 5.13 ?

3. Mar 11, 2016

### foo9008

not really

4. Mar 11, 2016

### BvU

It all hinges on $$\Delta Q << Q \ \ \Rightarrow \ \ (Q + \Delta Q)^2 = Q^2 + 2 Q\, \Delta Q + (\Delta Q)^2\approx Q^2 + 2 Q \Delta Q$$ which is satisfied (maybe not in the first iteration, but later on it is) -- $\Delta Q$ gets smaller and smaller if you do things right.
(I filled in n = 2 for simplicity)

You could also see this as a differentiation ( ${dh\over dQ} = 2KQ {\rm \ \ or \ \ } \Delta h = 2 Q \Delta Q$ ) and then the method is basically the Newton method

5. Mar 11, 2016

### foo9008

removed

6. Mar 12, 2016

??