Answer
$P_2=2.25\times10^5~Pa$
Work Step by Step
Convert units:
${dV\over dt}=(7200~cm^3/s)({1~m\over 100~cm})^3=0.0072~m^3/s$
$r_1=4~cm=0.04~m$
$r_2=2~cm=0.02~m$
$P_1=2.4\times10^5~Pa$
Find $v_1$:
$v_1={dV/dt \over A}={0.0072 ~m^3/s\over \pi (0.04~m)^2}=1.43~m/s $
Find $v_s$ using Fluid Continuity Equation:
$A_1v_1=A_2v_2$
$v_2={\pi(0.04~m)^2(1.43~m/s) \over \pi(0.02~m)^2}=5.73~m/s$
Since we know that the pipe is horizontal, the terms with vertical components will be zero in Bernoulli's Equation:
$P_2=P_1+{1\over2}\rho (v_1^2-v_2^2)$
$P_2=(2.4\times10^5~Pa)+{1\over2}(1000~kg/m^3)[(1.43~m/s)^2-(5.73~m/s)^2]=2.25\times10^5~Pa$
