Different locations of a pump in a tube I'm confused about pumps in fluid dynamics.
As far as I understand, the basic effect of a pump which deliver a power $\mathcal{P}$ can be described with modified bernoulli equation between a point $A$ before the pump and a point $B$ after the pump.
$$(p_A+\frac{1}{2} \rho v_A^2 +\rho g h_A)\cdot Q +\mathcal{P}=( p_B +\frac{1}{2} \rho v_B^2 +\rho g h_B)\cdot Q=\mathrm{constant}\tag{1}$$
Now my specific problem is: does it really matter where the pump is located inside the tube?
In the picture the pump is located ad height $B$, but, if it was located at $A$ or $C$, would something change? That is, would the fluid have different speed at the top when it flows out of the tube?

My answer would be no, since I can place the pump in $B$, but I can also use Bernoulli equation between $A$ and $B$, which says that the $\mathrm{constant}$ in the equation is the same for $A$ and $B$, so the situation in the picture is equivalent to one with the pump in $A$.
So if this is true I can use $(1)$ between any poin before the pump and any point after the pump, regardless the distance from the pump itself.
Can the reasoning be correct? 
 A: 
In the picture the pump is located ad height BB, but, if it was located at AA or CC, would something change? That is, would the fluid have different speed at the top when it flows out of the tube?

In a nutshell: no.

Bernoulli's equation, between the points $1$ and $2$, is as follows, where $p$ is the pressure supplied by the pump:
$$p_1+\frac{1}{2} \rho v_1^2 +\rho g h_1+p=p_2 +\frac{1}{2} \rho v_2^2 +\rho g h_2$$
Now it is important to understand the suffixes $1$ and $2$.
At point $1$ (the surface of the lower tank), $p_1=p_0$, where $p_0$ is atmospheric pressure.
Similarly, assuming the point $2$ gives to open air, then $p_2=p_0$.
In addition, is we assume the bottom tank's surface area is much larger than the cross section of the pipe, then $v_1 \ll v_2$.
After minimal reworking, the equation then simplifies to:
$$v_2\approx \sqrt{2\big[\frac{p}{\rho}-g(h_2-h_1)\big]}$$
So the placement of the pump is immaterial, only the pressure it delivers and the difference in height between the points $1$ and $2$ matter. The equation doesn't depended on the distances $|AB|$ or $|BC|$ at all.
A: I think it does matter where you place the pump.
Regardless of how powerful the pump is, the minimum pressure it can create at the input is zero - a perfect vacuum.  The pressure pushing the fluid up to the pump is then the atmospheric pressure.  
If the fluid is water, the maximum distance the atmosphere can pump it up to is about 10m.  So the pump must be located no more than 10m above the water level. Of course, this will not matter if $h < 10m$.
