Bournalli's Equation homework problem

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Homework Help Overview

The problem involves fluid dynamics, specifically applying Bernoulli's equation to analyze the pressure changes in a fluid flowing through a horizontal pipe with varying diameters. The original poster seeks to determine the pressure at a second point in the pipe based on the given parameters.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of Bernoulli's equation to find the pressure at Point 2, questioning the relationship between pressure and velocity in the context of fluid flow. There is also a consideration of the implications of pressure differences on physical impact.

Discussion Status

Some participants have confirmed the calculations presented, while others are exploring the implications of pressure versus velocity on the perceived force of the fluid. The discussion reflects a mix of agreement and questioning regarding the intuitive understanding of the results.

Contextual Notes

Participants are grappling with the counterintuitive nature of pressure and velocity relationships in fluid dynamics, particularly in the context of real-world applications such as the force of water from hoses of different diameters.

jan2905
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A fluid of density (rho) flows through a horizontal pipe with negligible viscosity. The flow is streamline with constant flow rate. The diameter of the pipe at Point 1 is d and the flow speed is v. If the diameter of the pipe at Point 2 is d/3, then the pressure at Point 2 is?



Bournalli's Equation (sp). I ended up getting P2=P1 - 40(rho)v^2. Correct?
 
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jan2905: That is correct; p2 = p1 - 40*rho*v^2.
 
would this mean that if i were hit with the liquid at the respective points...

p1 would hurt more than p2? that would mean that a large mouth waterhose has more force than a small mouth... that is not correct though.
 
jan2905: I think water exiting a small-mouth water hose at point 2 would probably hurt more, because it has a much higher velocity than the water at point 1. Both streams would be at atmospheric pressure immediately upon exit from the nozzle.
 
but we deduced that p1 would have more pressure therefore hurting more. this math seems to be counterintuitive.
 

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