Answer
The pressure at the lower level is $~~2.6\times 10^5~Pa$
Work Step by Step
We can find the speed at the lower level:
$v_2~A_2 = v_1~A_1$
$v_2 = \frac{v_1~A_1}{A_2}$
$v_2 = \frac{(5.0~m/s)(4.0~cm^2)}{8.0~cm^2}$
$v_2 = 2.5~m/s$
We can find the pressure at the lower level:
$P_2+\frac{1}{2}\rho v_2^2+\rho g y_2 = P_1+\frac{1}{2}\rho v_1^2+\rho g y_1$
$P_2 = P_1+\frac{1}{2}\rho (v_1^2-v_2^2)+\rho g (y_1-y_2)$
$P_2 = (1.5\times 10^5~Pa)+(\frac{1}{2})(1000~kg/m^3) [(5.0~m/s)^2-(2.5~m/s)^2]+(1000~kg/m^3)(9.8~m/s^2) (10~m)$
$P_2 = 2.6\times 10^5~Pa$
The pressure at the lower level is $~~2.6\times 10^5~Pa$
