Water Pressure

Hi,

I am working on this water pressure problem,



given:

v_A = 2.0 [itex]\frac{m}{s}[/itex]
gauge pressure_A = 50 kPa
the view is from above, no height changes

find: gauge pressure @ B

so,

[itex]A_Av_A=2(A_Bv_B)[/itex]
[itex]1.5*10^{-2}m^2(2.0\frac{m}{s})=2(5*10^{-3}m^2v_B)[/itex]
[itex]v_B=9.0\frac{m}{s}[/itex]

Bernoulli's equation (w/o the [itex]\rho gh[/itex] components bc height is constant):

[itex]p_A+\frac{1}{2}\rho _Av_A^2=p_B+\frac{1}{2}\rho _Bv_B^2[/itex]

My question is, how come the right side of the equation is not [itex]2(p_B+\frac{1}{2}\rho _Bv_B^2)[/itex]? Shouldn't there be a coefficient of two, because the pipe splits in half?

Thanks