Pressure difference in decreasing diameter tube

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Discussion Overview

The discussion revolves around calculating the pressure difference (ΔP) in a pipe with a decreasing diameter through which helium flows. Participants explore the application of Bernoulli's equation and the continuity equation, considering the assumptions of incompressible and inviscid flow. The conversation includes attempts to convert mass flow rate to volumetric flow rate and to derive flow velocities.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Participants discuss the need to convert mass flow rate (0.30 kg/s) to volumetric flow rate to find velocities, with some suggesting dividing by density (0.166 kg/m³) to achieve this.
  • One participant calculates a volumetric flow rate of 1.807 m³/s based on the mass flow rate and density, raising questions about the validity of this value.
  • There is a discussion about the relationship between Bernoulli's equation and the continuity equation, with some asserting that both can be used together without conflict.
  • One participant expresses concern that their calculated pressure increase of 58 Pa seems low, indicating uncertainty about the results.

Areas of Agreement / Disagreement

Participants express differing views on the calculations and assumptions regarding the application of Bernoulli's equation and the conversion of flow rates. No consensus is reached on the correct approach or the validity of the calculated pressure difference.

Contextual Notes

There are unresolved issues regarding the conversion of mass flow rate to volumetric flow rate and the implications of using Bernoulli's equation in this context. The assumptions of incompressibility and inviscid flow are also critical to the discussion but are not universally accepted as straightforward.

MonkeyMouse
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Homework Statement



Helium at 20°C passes through a pipe with an initial diameter of .3 meters decreasing to .25 meters. The helium flows at .30 kg/s and an initial pressure of 200 kpa. Find the difference in pressure ΔP across the decreasing section. Assume incompressible and inviscid flow.

From known values of helium at 20°C: Density= 0.166 kg/m3, Specific weight= 1.63 N/m3,

Homework Equations



Bernoulli eq: (p1/\gamma)+(V12/2g)+Z1=(p2/\gamma)+(V22/2g)+Z2

V=Q/A

The Attempt at a Solution


Not a free jet situation.
Z1 and Z2 = 0 due to no elevation change

A1=(\pi.3m2)/4=.0706m2
A2=(\pi.25m2)/4=.0491m2

My hang up is when I get to this point, Q=.30 Kg/s and I am unsure how to convert this to m3/s in order to find V1 and V2 in terms of m/s? Also once I have this I am unsure of the unit conversions I would need to return P2 in kpa in order to find the pressure difference?
 
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MonkeyMouse said:

Homework Statement



Helium at 20°C passes through a pipe with an initial diameter of .3 meters decreasing to .25 meters. The helium flows at .30 kg/s and an initial pressure of 200 kpa. Find the difference in pressure ΔP across the decreasing section. Assume incompressible and inviscid flow.

From known values of helium at 20°C: Density= 0.166 kg/m3, Specific weight= 1.63 N/m3,

Homework Equations



Bernoulli eq: (p1/\gamma)+(V12/2g)+Z1=(p2/\gamma)+(V22/2g)+Z2

V=Q/A

The Attempt at a Solution


Not a free jet situation.
Z1 and Z2 = 0 due to no elevation change

A1=(\pi.3m2)/4=.0706m2
A2=(\pi.25m2)/4=.0491m2

My hang up is when I get to this point, Q=.30 Kg/s and I am unsure how to convert this to m3/s in order to find V1 and V2 in terms of m/s? Also once I have this I am unsure of the unit conversions I would need to return P2 in kpa in order to find the pressure difference?

You use the continuity relation and assume that the volume of helium flowing into the pipe is the same as the volume flowing out of the pipe. Since the helium is assumed incompressible, the density is constant in the pipe. You know the cross-sectional area of the pipe, so you should be able to calculate the flow velocity of the helium which satisfies the continuity relation thru the pipe.
 
what if your required to use Bernoullis eq? Would you divide the mass flow by the density for the volumetric flow to solve for velocity?

There for: (0.30kg/s)/(0.166kg/m^3)=1.807m^3/s
 
Last edited:
MonkeyMouse said:
what if your requied to use Bernoullis eq? would you decide the mass flow by the density for the volumetric flow to solve fir velocity?
Sure. Why not?
 
MonkeyMouse said:
what if your requied to use Bernoullis eq? would you decide the mass flow by the density for the volumetric flow to solve fir velocity?

Using Bernoulli does not necessarily mean that the continuity relation is invalid. After all, Bernoulli relates the total energy of the flow at one point to another. All the continuity relation does is state that fluid is not created or destroyed between these same points. Both relations are complementary.
 
Has anyone worked, or could anyone work through this problem? I'm coming up with an increase of 58 Pa which seems low?
 

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