Why tubes with lower cross sectional area has lower pressure than the tubes with high cross sectional area? The tube with lower cross sectional area has a lower pressure than the tube with high cross sectional area, right? Why is that, how can I understand this intuitively and using bernoulli principle (or other principle)?

 A: You know that the mass flow through the two pipes is equal.  You can write one equation for the mass flow through the first pipe, and another for the mass flow through the second pipe, in terms of the inlet pressure, the junction pressure, and the outlet pressure.  That pair of equations can be solved together for the junction pressure in terms of the inlet pressure and the outlet pressure. The pressure in each pipe will drop linearly from its input to its own output end.
A: I can understand now, I dont know how to delet the post, so I am posting the answer. From conservation of mass $Av=ctte$ and from Bernoulli principle, with less velocity, higher the pressure. So with higher area -> higher the pressure. This does not contradict, however, $P=F/A$, because the force decreases with the decreasing of area too.
A: You can understand this using mass conservation and Bernoulli's principle, between sections $1$ and $2$ in your figure.
Mass conservation:
$$ V_1A_1 = V_2A_2$$
This implies that $V_2 = V_1 \frac{A_1}{A_2}$, so we can clearly see that $V_2 < V_1$. We can relate the velocities to pressure using momentum conservation (it's convenient to use the integrated momentum conservation, or Bernoulli's equation here).
Bernoulli's principle:
$$ P_1 + \frac{1}{2}V_1^2 =  P_2 + \frac{1}{2}V_2^2 $$
This implies that 
$$ P_2 = P_1 + \frac{1}{2} (V_1^2 - V_2^2) $$
If you plug in the $V_2$ we found, you'll see that $P_2 < P_1$. 
In general, Bernoulli's principle predicts that regions of slow moving fluid have higher pressures that regions of fast moving fluid, and vice versa.
