Fluid dynamics continuity equation

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SUMMARY

The discussion focuses on solving a fluid dynamics problem involving the continuity equation for air flow through a cylindrical heating tube. The required air velocity is 3 m/s to heat a rectangular space measuring 12 m by 10 m by 2.5 m, with a refresh rate of every 15 minutes. The initial calculation for the tube's radius yielded an incorrect result of 0.132 m, while the correct radius is determined to be 0.1881 m after applying the correct area formula for a circle. The continuity equation used is A1 x v1 = A2 x v2, leading to the necessary adjustments in calculations.

PREREQUISITES
  • Understanding of fluid dynamics principles
  • Familiarity with the continuity equation
  • Knowledge of cylindrical geometry and area calculations
  • Basic algebra for solving equations
NEXT STEPS
  • Study the derivation and applications of the continuity equation in fluid dynamics
  • Learn about the properties of cylindrical shapes and their relevance in fluid flow
  • Explore the concept of volumetric flow rate and its calculations
  • Investigate common errors in fluid dynamics problems and how to avoid them
USEFUL FOR

This discussion is beneficial for students studying fluid dynamics, engineers working with HVAC systems, and anyone involved in thermal management and airflow calculations.

Nanu Nana
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Homework Statement


Through a (cylindrical) heating tube, warm air has to flow with a velocity of 3m/s in order to heat a rectangular spacewhich is 12 m long, 10 m wide and 2.5 m high. How large the radius of the tube should be if the air in the room get refreshed every 15 minutes ? Assume that the air-density in the tube and in the room are equal.

Homework Equations


Continuity equation
A1 x v1 = A2 x v2[/B]

The Attempt at a Solution


Flowrate = Volume/ t V/t = A x v
Flowrate = 12x10x2.5 = 300 m3 / 900 s = 0.33
0.33 = A2 x 3m/s
A2= 0.111 m^2
So to find the radius you have to use area of cilinder
A=pi x 2x (r)^2
0.111= pi x 2x (r)^2
r= 0.132 m why do i get this answer ?? . Its wrong .answer has to be 0.1881 [/B]
 
Physics news on Phys.org
What is the equation for the area of a circle?
 
A= pi x (r)^2
Now its correct
Thank you
 

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