Bernoulli Equation - fluid mechanics question

[LauraMorrison]

Hi, I am a first year studying mechanical engineering and I am having trouble understanding bernoulli equation. This is the first question in the tutorial and I can't seem to get the right answer.

Water flows through the pipe contraction shown
in the figure below. For the given 0.2 m
difference in manometer level, determine the
flowrate as a function of the diameter of the small
pipe, D.
(Ans: 1.56D2 m3/s)



From the solution given by my lecturer, it says that z₁ = z₂ .. this will probably sound really stupid but what height does z actually represent?
I know that there is a stagnation point at the pitot tube coming from the manometre so this means that v₁ = 0 .. is that correct? The solutions also say that p₁ = $\gamma$h₁ .. how can this be? I thought that pressure = Force x Area?

If someone could explain the answer to me it would really help a lot.

Thanks!

 

[SteamKing]

For fluids, pressure = rho * g * h, where
rho - mass density of fluid (kg/m^3)
g - acceleration due to gravity (9.81 m/s^2)
h - depth of fluid at point where pressure is measured (m)
rho*g = gamma - this is the weight density of the fluid, (N / m^2)

Pressure has units of kg-m^2/(m^3s^2), which by rearranging becomes:
(kg-m/s^2)*(m/m^3) = N/m^2, which is units of force / area.

This is known as Pascal's Law.

 

[LauraMorrison]

Thank you! That helps quite a bit!