Answer
The reading on the top pressure gauge is 110 kPa
Work Step by Step
We can use Bernoulli's equation to find the reading $P_2$ on the top pressure gauge. We can use $\rho = 900~kg/m^3$ for the density of oil.
$P_2 +\frac{1}{2}\rho v_2^2+\rho g h_2 = P_1 +\frac{1}{2}\rho v_1^2+\rho g h_1$
$P_2 = P_1 +\frac{1}{2}\rho (v_1^2-v_2^2)+\rho g (h_1-h_2)$
$P_2 = (2\times 10^5~Pa) +\frac{1}{2}(900~kg/m^3) [(2.0~m/s)^2-(3.0~m/s)^2]+(900~kg/m^3)(9.80~m/s^2)(-10~m)$
$P_2 = (2\times 10^5~Pa) -(2250~Pa)-(88,200~Pa)$
$P_2 = 1.1\times 10^5~Pa = 110~kPa$
The reading on the top pressure gauge is 110 kPa.
