Calculate h if the fluid in the manometer is mercury

[xCuzIcanx]

Homework Statement

A venture flow-meter can be designed as
shown in the figure. At position 1 the
velocity is 0.5 m/s, and pressure is 1.3 bar.
The cross section area at 1 is two times the
area at 2. The fluid inside the manometer
has a density ρ, and the fluid column has a
high h as shown in the figure.
Assume the temperature is 20oC,
conducting the following analysis:
1) Derive the equation h as a function
of ρ.
2) Calculate h if the fluid in the
manometer is mercury

Picture is attached.

To be honest, I have no idea what I'm suppose to do. Please help.

 

[SteamKing]

It's actually a 'venturi' flow meter.

Hint: apply Bernoulli's theorem to the flow.

 

[xCuzIcanx]

It's actually a 'venturi' flow meter.

Hint: apply Bernoulli's theorem to the flow.

So the flow meter would have the equation of the Bernoulli's Equation for fluids and the manometer would have the equation deltaP=rho*g*h. But how would I find the equation with those two separate one?

 

[Chestermiller]

So the flow meter would have the equation of the Bernoulli's Equation for fluids and the manometer would have the equation deltaP=rho*g*h. But how would I find the equation with those two separate one?

You need to use the Bernoulli equation to calculate the pressure difference between the two points in the flow. Then you need to use the hydrostatic equation to determine the difference in height in the manometer for the calculated pressure difference.