Solving Bernoulli Principle Homework: Water Flows in Pipe

In summary, the problem involves water flowing upward through a pipe at a rate of 96 L/Min. The pressure at the lower end is 80kPa and the density of water remains constant throughout the tube. The height of the lower end is given as 10m and the upper end as 13m. The attempt at a solution includes using the continuity equation to find the velocity, but since the area is not given, this method is unsuccessful. An alternative attempt involves using the Bernoulli equation, but further information, such as the diameter and orientation of the pipe, is needed.
  • #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
I can't see your diagram so if you could attached it maybe I can help.

I refer to the bernoulli's theorem as energy per unit weight:
(P_1/(rho*g))+(V_1^2/2g)+h1 = (P_2/(rho*g))+(V_2^2/2g)+h2
Q = 1.6x10^-3 m^3/s

By inspection of the pipeline, is it tapered or is the diameter constant? If it is constant what would be the relationship between V_1 and V_2?

A change of diameter should however should be stated if there is one... Is it a horizontal, angled or vertical pipe?
 

FAQ: Solving Bernoulli Principle Homework: Water Flows in Pipe

What is the Bernoulli Principle?

The Bernoulli Principle states that as the speed of a fluid (such as water) increases, the pressure exerted by the fluid decreases. This principle is based on the conservation of energy, which states that the total energy of a system remains constant.

How does the Bernoulli Principle apply to water flowing in a pipe?

In a pipe, the water flows at different speeds due to changes in the pipe's diameter. According to the Bernoulli Principle, as the water flows through a narrower section of the pipe, its speed increases and the pressure decreases. This decrease in pressure can be observed as a decrease in the water level in a vertical pipe.

What factors affect the application of the Bernoulli Principle in water flow?

The Bernoulli Principle is affected by the diameter of the pipe, the velocity of the water, and the density of the fluid. It also assumes that the fluid is incompressible and flowing in a steady, non-turbulent manner.

Can the Bernoulli Principle be used to calculate the pressure at different points in the pipe?

Yes, the Bernoulli Principle can be used to calculate the pressure at different points in the pipe. By measuring the velocity of the water and the diameter of the pipe at different points, the pressure can be calculated using the Bernoulli equation.

How is the Bernoulli Principle used in real-life applications?

The Bernoulli Principle is used in various real-life applications such as in airplane wings, carburetors, and water fountains. It is also used in industrial settings to measure the flow rate of liquids and gases in pipes. In everyday life, the Bernoulli Principle can be seen in action when blowing air over a piece of paper to lift it up or when using a straw to drink a beverage.

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