Problem $2.$ A Venturi meter is used to measure the pressure drop going through a choke point

$($constricted section$)$ of the pipe diagram shown below. Here, vegetable oil $($in blue$)({}_0=1200$

$k\frac{g}{m^3})$ is transported at a velocity of $4\frac{m}{s}$ before it hits the choke point. The crude oil is

incompressible, and the flow is at steady state.

a$)(3$ pt$.)$ Determine the velocity of the fluid in the constricted zone $($point $2)$ in units of $\frac{m}{s}.$

b$)(3$ pt$.)$ Show how you can simplify Bernoulli's equation to determine the pressure drop.

Solve for $P_1-P_2$ in units of $Pa.$

c$)(4$ pt$.)$ A pressure gauge filled with mercury $($in white$)({}_m=13600\frac{kg}{m^3})$ is attached and

records the pressure drop. What is the height difference in units of $[$m$]?$