How Is the Throat's Cross-Sectional Area Determined Using Bernoulli's Principle?

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SUMMARY

The cross-sectional area of the throat in a duct system can be determined using Bernoulli's Principle and the equation of continuity. Given an air velocity of 100 mph and a pressure difference of 7 inches of water, the calculated throat area is 2.57 square feet. The incompressibility of air and its density of 0.002378 slug per cubic feet are critical factors in this calculation. Understanding these principles allows for accurate fluid dynamics analysis in duct systems.

PREREQUISITES
  • Bernoulli's Principle
  • Equation of Continuity
  • Fluid dynamics fundamentals
  • Basic pressure measurement techniques
NEXT STEPS
  • Study the derivation of Bernoulli's equation for horizontal flow
  • Explore the application of the equation of continuity in fluid systems
  • Learn about pressure measurement techniques using U-tube manometers
  • Investigate the effects of air density on flow calculations
USEFUL FOR

Students and professionals in engineering, particularly those focusing on fluid dynamics, HVAC systems, and aerodynamics, will benefit from this discussion.

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Homework Statement



air is flowing horizontally at a speed of 100 mph through a duct 4 square feet in cross section. the duct gradually narrows down to a throat section. if a U-tube shows a difference in pressure between the throat and main sections of 7 inch of water, what is the cross sectional area of the throat? (assume that the air is incompressible and has a density of 0.002378 slug per cubic feet)

Homework Equations


The Attempt at a Solution


i already have the final answer and it is

2.57 square/feet

but i need the solution... T_T.. help

Homework Statement


Homework Equations


The Attempt at a Solution

 
Physics news on Phys.org
For a horizontal pipe what is Bernoulli's equation reduced to?

When you get that formula you can find the velocity leaving the throat section.

Do you know the equation of continuity?
 

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