Find the gauge pressure at a second point in the line

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SUMMARY

The discussion focuses on calculating the gauge pressure at a second point in a horizontal pipeline using Bernoulli's equation. Given the initial conditions of water speed at 2.50 m/s and gauge pressure of 1.80 * 10^5 Pa, the problem emphasizes the relationship between area and velocity, where doubling the cross-sectional area results in halving the flow velocity. The key takeaway is that by applying the principles of fluid dynamics, specifically the Continuity equation and Bernoulli's equation, one can derive the gauge pressure at the second point without needing the radius of the pipe.

PREREQUISITES
  • Understanding of Bernoulli's equation
  • Familiarity with the Continuity equation in fluid dynamics
  • Basic knowledge of gauge pressure and fluid properties
  • Concept of incompressible flow in fluids
NEXT STEPS
  • Study Bernoulli's equation in detail, including its applications
  • Learn about the Continuity equation and its implications in fluid flow
  • Explore the concept of incompressible fluids and their properties
  • Practice problems involving gauge pressure calculations in various fluid systems
USEFUL FOR

This discussion is beneficial for students and professionals in engineering, particularly those specializing in fluid mechanics, as well as anyone involved in hydraulic system design and analysis.

CollectiveRocker
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I have been going over this problem for at least 3 hours now, without any sign of improvement. I was wondering if you guys could at least point me in the direction of something I missed. Problem: At a certain point in a horizontal pipeline, the water's speed is 2.50 m/s and the gauge pressure is 1.80 * 10^5 Pa. Find the gauge pressure at a second point in the line if the crosssection area at the second point is twice that of the first. Now I realize the critical part of this problem is finding the area, thus Pressure = Force/Area. But how do you find the area at point 1 without knowing the radius? Is there another formula for area which i don't know>
 
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CollectiveRocker said:
I have been going over this problem for at least 3 hours now, without any sign of improvement. I was wondering if you guys could at least point me in the direction of something I missed. Problem: At a certain point in a horizontal pipeline, the water's speed is 2.50 m/s and the gauge pressure is 1.80 * 10^5 Pa. Find the gauge pressure at a second point in the line if the crosssection area at the second point is twice that of the first. Now I realize the critical part of this problem is finding the area, thus Pressure = Force/Area. But how do you find the area at point 1 without knowing the radius? Is there another formula for area which i don't know>

This looks like a job for Bernoulli's eq. to me, not pressure = force/area. The trick is that you need to know that when you double the area, you halve the flow velocity. This happens because water is incompressible, so velocity*area = constant. So know you know the pressure and velocity at point 1, and you can figure out the velocity at point 2, thus you can compute the pressure with Bernoulli's eq.


http://hyperphysics.phy-astr.gsu.edu/hbase/pber.html
 
So are P1 & P2 = gauge pressure, y1 = 0, y2 = 0.
 
rho * Area * Velocity = constant.. in your case rho 1 = rho 2 since density of water does not change.. so there you go...
 
Yes, a combination of Continuity, and Bernoulli, should get you there.
 

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