Pressure difference in a horizontal constant area pipe

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SUMMARY

The discussion focuses on analyzing pressure differences in a horizontal pipe with constant area under non-steady state conditions. Key equations referenced include the mass flow conservation and Bernoulli's principle, specifically noting that Bernoulli's assumptions apply to inviscid flow. The participants conclude that while mass flow in equals mass flow out, friction leads to head loss and a decrease in pressure, impacting fluid velocity. The confusion arises from distinguishing between steady and unsteady flow conditions, particularly regarding the effects of friction on velocity and pressure.

PREREQUISITES
  • Understanding of Bernoulli's equation and its assumptions
  • Knowledge of fluid dynamics principles, particularly mass flow conservation
  • Familiarity with concepts of head loss due to friction in viscous fluids
  • Basic grasp of steady vs. unsteady flow conditions
NEXT STEPS
  • Study the implications of Bernoulli's equation in real-world applications
  • Learn about head loss calculations in pipe flow using the Darcy-Weisbach equation
  • Explore the differences between laminar and turbulent flow regimes
  • Investigate the effects of viscosity on fluid motion and pressure changes
USEFUL FOR

Students and professionals in mechanical engineering, fluid mechanics, and anyone involved in analyzing fluid flow in piping systems.

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Homework Statement



see attachment

Homework Equations


not sure if these are applicable because i don't think its steady state anymore
mass flow in=mass flow out
sum of forces in x direction= rate of momentum in-rate of momentum out
bernoulli's p+0.5ρ(v^2)= constant

The Attempt at a Solution


2.2a No
2.2b true, true, false as bernoullis assumption states inviscid flow, true if the given equations are true, true as the fluid is slowing down so resultant force is going in the left so pressure force at 2 is greater then pressure 1.
I am confused on making the correct assumptions could someone help me please?
 

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2B is false. The amount of liquid entering the pipe has to be equal to the amount of liquid exiting it in steady operation. Friction won't cause a decrease in velocity (at the wall the liquid isn't moving anyway for viscous fluids). The friction will cause a head loss though. So you see the impact in a decrease in pressure This energy is converted into heat. Maybe now you can get the other parts as well?
 

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