Volume flow rate and mass flow rate

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SUMMARY

The discussion focuses on calculating the flow velocity, volume flow rate, and mass flow rate in a pipe with a tapering section. The pipe's diameters are 410mm and 260mm, with an incompressible fluid density of 1000 kg/m³ and a flow velocity of 2 m/s in the smaller diameter. The user initially miscalculated the flow rate by using diameters instead of areas. The correct calculations involve determining the cross-sectional areas using the formula A = π(d/2)² and applying the continuity equation for incompressible flow.

PREREQUISITES
  • Understanding of fluid dynamics principles, specifically the continuity equation.
  • Knowledge of cross-sectional area calculations for circular pipes.
  • Familiarity with the concepts of volume flow rate and mass flow rate.
  • Basic proficiency in algebra for manipulating equations.
NEXT STEPS
  • Learn how to calculate the cross-sectional area of a circle using A = π(d/2)².
  • Study the continuity equation in fluid dynamics to understand flow relationships.
  • Explore the concept of incompressible flow and its implications on fluid behavior.
  • Investigate practical applications of flow rate calculations in engineering scenarios.
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Students and professionals in engineering, particularly those specializing in fluid mechanics, as well as anyone involved in designing or analyzing piping systems.

MNWO
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Hello there, so I have answered my question from fluid systems but the answer doesn't look right ;/ and I have no idea what have I done wrong. Can you please check and correct where it's wrong ? ;) here is the question:
A pipe contains a gradually tapering section in which its diameter decreases from 410mm to 260mm. The pipe contains an incompressible fluid of density 1000kgm- 3 and runs full. If the flow velocity is 2ms in the smaller diameter, determine the velocity in the larger diameter, the volume flow rate and the mass flow rate.


My calculations:
A1=260mm=0.26m
V1=2ms
A2=410mm=0.41m
V2=?
Flow rate (Q)=A1 x V1 which is equal to A2 x V2
0.26 x 2=0.52 m/s 3 (metres per second cubed)
V2= Q/A2 = 0.52/0.41
V2=1.26 m/s 3
mass flow rate (M)= Density x Q = 1000x 0.52
M=520 kg/s

I would really aprreciate any help :)
 

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MNWO said:
Hello there, so I have answered my question from fluid systems but the answer doesn't look right ;/ and I have no idea what have I done wrong. Can you please check and correct where it's wrong ? ;) here is the question:
A pipe contains a gradually tapering section in which its diameter decreases from 410mm to 260mm. The pipe contains an incompressible fluid of density 1000kgm- 3 and runs full. If the flow velocity is 2ms in the smaller diameter, determine the velocity in the larger diameter, the volume flow rate and the mass flow rate.


My calculations:
A1=260mm=0.26m
V1=2ms
A2=410mm=0.41m
V2=?

Be careful here. You were given the diameters of the pipe, not the areas. How does the area of a pipe depend on its diameter?

Flow rate (Q)=A1 x V1 which is equal to A2 x V2
0.26 x 2=0.52 m/s 3 (metres per second cubed)
V2= Q/A2 = 0.52/0.41
V2=1.26 m/s 3
mass flow rate (M)= Density x Q = 1000x 0.52
M=520 kg/s

I would really aprreciate any help :)

See comment above.
 
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SteamKing said:
Be careful here. You were given the diameters of the pipe, not the areas. How does the area of a pipe depend on its diameter?
See comment above.[/QUOT
Ah okay, i know what's wrong now. Thank you for that
 

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