Bernoulli Equation - fluid mechanics question

In summary, the conversation was about a first year mechanical engineering student struggling with understanding the Bernoulli equation and a specific problem involving water flow through a pipe contraction. The solution provided by the lecturer involved understanding the concept of z as the height of fluid, and the relationship between pressure, density, and gravity known as Pascal's Law.
  • #1
LauraMorrison
26
0
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 = [itex]\gamma[/itex]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!
 

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  • #2
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.
 
  • #3
Thank you! That helps quite a bit!
 

1. What is the Bernoulli Equation?

The Bernoulli Equation is a fundamental equation in fluid mechanics that describes the relationship between pressure, velocity, and elevation in a fluid flow. It states that as the velocity of a fluid increases, the pressure decreases, and vice versa.

2. How is the Bernoulli Equation used in real-world applications?

The Bernoulli Equation is used in a variety of real-world applications, including aerodynamics, hydraulics, and HVAC systems. It can be used to calculate the lift force on an airplane wing, the flow rate of water through a pipe, and the air velocity in a ventilation system.

3. What are the assumptions made in the Bernoulli Equation?

The Bernoulli Equation makes several assumptions, including that the fluid is incompressible, inviscid, and steady-state. It also assumes that the flow is irrotational, meaning that the fluid particles do not rotate as they move through the flow.

4. Can the Bernoulli Equation be applied to all fluid flows?

No, the Bernoulli Equation can only be applied to certain types of fluid flows, including steady, incompressible, and inviscid flows. It is not applicable to turbulent or compressible flows.

5. How is the Bernoulli Equation derived?

The Bernoulli Equation is derived from the principles of conservation of mass and conservation of energy. It can also be derived from the Navier-Stokes equations, which describe the motion of fluids.

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