Solving Bernoulli's Equation for Fluid Mechanics in Ethanol Pipe

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Discussion Overview

The discussion revolves around solving Bernoulli's equation in the context of fluid mechanics, specifically for ethanol flowing through a tapered horizontal pipe. Participants are exploring how to calculate the volume flow rate given specific parameters such as pressure difference, density, and cross-sectional areas.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant presents a problem involving ethanol flowing through a pipe and requests assistance in calculating the volume flow rate.
  • Another participant suggests writing out Bernoulli's equations and compiling the necessary data for calculations.
  • A participant states the Bernoulli equation and provides some known values, including pressure difference and density, but expresses uncertainty about how to find the volume flow rate.
  • One participant questions the method used to derive the velocity difference (v2 - v1 = 3.2 m/s) and notes that it was calculated using the Venturi equation.
  • Another participant clarifies that the Venturi equation is a specific application of Bernoulli's equation and emphasizes the importance of mass flow conservation in the analysis.
  • A hint is provided regarding the relationship between mass flow, density, cross-sectional area, and velocity.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the correct approach to solve the problem, with some advocating for the use of Bernoulli's equation while others suggest the Venturi equation. The discussion remains unresolved regarding the best method to calculate the volume flow rate.

Contextual Notes

Participants have not fully detailed all assumptions or previous calculations, and there is some ambiguity regarding the application of different equations in this context.

escobar147
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Ethanol of density 791 kgm-3 flows smoothly through a horizontal pipe that tapers in cross-sectional area from A1= 1.20 x 10-3 m2 to A2=A1/2. The pressure difference between the wide and narrow sections of the pipe is 4120 Pa. What is the volume flow rate of the ethanol?


(Ans.: 2.24 x 10-3 m3s-1)

how is this worked out? any help would be massively appreciated.

 
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Write your Bernoulli equations and start compiling the data to plug into them. Let's see some work!
 


ok

bernoullis equation states that:

P1 + ρgh1 + 1/2ρ(v1)^2 = P2 + ρgh2 + 1/2ρ(v2)^2

now i believe from some other calculations that
v2 - v1 = 3.2 m/s

and we know that:

p2 - p1 = 4120 pa
ρ = 791 kgm-3
g = 9.81
the volume flow rate is given by: cross sectional area x flow velocity

but i just can't see how to find the volume flow rate with the given information
 


i'm starting to think I'm using the wrong equation altogether...
 


What other calculation did you do to get v2 - v1 = 3.2 m/s? It's not shown.
 


sorry i forgot i used the venturi equation:

p1 - p2 = ρ/2(v2^2 - v1^2)
 


The venturi equation is a special form of the Bernoulli equation. What you should use in addition to the Bernoulli equation is the fact that the mass flow of alcohol into the pipe is the same as the mass flow leaving the pipe.
 


Hint: the mass flow past a point = Rho * Area * velocity
 

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