Bernoulli Principle: Homework Solution

In summary, the problem involves water flowing upward through a pipe at a given rate and pressure. The objective is to find the velocity at both ends of the pipe and the pressure at the upper end. The continuity equation and Bernoulli's equation are used in the attempt to find a solution, but additional information, such as the diameter or radius of the pipe, is needed to solve the equations effectively.
  • #1
srollin6
2
0

Homework Statement



Water Flows upward throw the pipe shown in the diagram at 96 L/Min. If the pressure at the lower end is 80kPa, find the velocity of the water is at both ends and the pressure at the upper end. Assume that the density of water remains constant throughout the tube and that h1= 10 m and h2 = 13m

Homework Equations


P1+ 1/2 ρv^2+gy1=P2+1/2ρv2^2+gy2

Continuity Equ:
A1V1=A2V2
(Tried to use this equation to hep me find the velocity but given their is no diameter or radius given to find the are it was a waste of time)

The Attempt at a Solution


volume flow rate up the pipe:
96L/min (1.0X10^3 cm^3/ 1.00L)(1.00m/100cm)^3(1.00min/60sec) = 1.6x10^3 m^3/s


Attempt to tried to use the Continuity Equation as substitution for one of the velocities:


A1V1=A2V2

V2(A2/A1)= V1

Substituting V1 in the Bernoulli Equation:
P1+1/2ρ(V2(A2/A1))^2+ρgy1=P2+1/2ρv2^2+gy2

2g(y^2-y1)=v2[1-(A2/A1)]

sqrt(2gh)/sqrt(1-(A2/A1)^2) =v2



Any help or guidance will be appreciated. Thank you.
 
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  • #2
srollin6 said:
... find the velocity of the water is at both ends ...
Something missing in the problem statement?
P1+ 1/2 ρv12+gy1=P2+1/2ρv22+gy2
Should be ρgy1, ρgy2, yes?
Continuity Equ:
A1V1=A2V2
(Tried to use this equation to hep me find the velocity but given their is no diameter or radius given to find the are it was a waste of time)
It doesn't mention any change in area, so presumably A1=A2.
Substituting V1 in the Bernoulli Equation:
P1+1/2ρ(V2(A2/A1))2+ρgy1=P2+1/2ρv22+gy2

2g(y^2-y1)=v2[1-(A2/A1)]
How do you get that last equation from the preceding one? What happened to P1 and P2?
 

What is the Bernoulli Principle?

The Bernoulli Principle, also known as the Bernoulli's equation, is a fundamental concept in fluid mechanics that explains the relationship between the speed of a fluid and its pressure. It states that as the speed of a fluid increases, its pressure decreases and vice versa.

What are the applications of the Bernoulli Principle?

The Bernoulli Principle has various applications in real life, including the design of airplane wings, ventilation systems, and carburetors for cars. It is also used in hydraulic systems, such as in dams and turbines, to generate electricity.

What are the factors that affect the Bernoulli Principle?

The Bernoulli Principle is affected by three main factors: fluid speed, fluid density, and the shape of the object through which the fluid is flowing. As the speed of the fluid increases, the pressure decreases. A higher fluid density also results in higher pressure. Additionally, the shape of the object can cause changes in the fluid speed and pressure.

How is the Bernoulli Principle related to lift?

The Bernoulli Principle is closely related to lift, which is the force that keeps an airplane in the air. As air flows over an airplane wing, it creates a difference in pressure, with the air moving faster over the curved top of the wing and slower underneath. This results in lower pressure on the top of the wing, causing lift to occur and allowing the plane to stay in the air.

What are some real-life examples of the Bernoulli Principle?

There are many real-life examples of the Bernoulli Principle, including the flow of water through a hose, the flight of a Frisbee, and the operation of a spray bottle. It also plays a role in the ventilation and air conditioning systems in buildings, as well as the design of race car spoilers. The principle is present in everyday activities, even if we may not realize it.

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