The velocity gradient at the wall normal to the wall

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SUMMARY

The discussion focuses on calculating the velocity gradient at the wall of a flat plate in hypersonic flow at Mach 10, as outlined in "Fundamentals of Aerodynamics" by John D. Anderson, Jr. The local shear stress at the wall is given as 282 N/m², with the gas temperature at standard sea level conditions. To solve this problem, understanding boundary layers and the temperature-dependent viscosity of air is essential. Participants emphasize the importance of accessing reliable data sources for physical properties to complete the calculations accurately.

PREREQUISITES
  • Understanding of boundary layer theory
  • Knowledge of shear stress and its implications in fluid dynamics
  • Familiarity with the concept of viscosity and its temperature dependence
  • Ability to interpret data from engineering resources
NEXT STEPS
  • Research the calculation of velocity gradients in fluid dynamics
  • Study the properties of air at varying temperatures using resources like the Engineering Toolbox
  • Learn about the implications of hypersonic flow on boundary layer behavior
  • Explore the use of computational fluid dynamics (CFD) tools for simulating hypersonic flows
USEFUL FOR

Aerospace engineers, fluid dynamics researchers, and students studying aerodynamics will benefit from this discussion, particularly those focused on hypersonic flow analysis and boundary layer calculations.

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Homework Statement


This problem is from "Fundamentals of aerodynamics" by John D. Anderson, Jr (Fifth edition, page 101):
Consider a flat plate at zero angle of attack in a hypersonic flow at Mach
10 at standard sea level conditions. At a point 0.5 m downstream from the
leading edge, the local shear stress at the wall is 282 N/m^2. The gas
temperature at the wall is equal to standard sea level temperature. At this
point, calculate the velocity gradient at the wall normal to the wall.

Homework Equations


Boundary layers

The Attempt at a Solution


18581812_1111291955643147_3221053711068545939_n.jpg
 
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dat said:

Homework Statement


This problem is from "Fundamentals of aerodynamics" by John D. Anderson, Jr (Fifth edition, page 101):
Consider a flat plate at zero angle of attack in a hypersonic flow at Mach
10 at standard sea level conditions. At a point 0.5 m downstream from the
leading edge, the local shear stress at the wall is 282 N/m^2. The gas
temperature at the wall is equal to standard sea level temperature. At this
point, calculate the velocity gradient at the wall normal to the wall.

Homework Equations


Boundary layers

The Attempt at a Solution


View attachment 205740
viscosity of air is a function of temperature. In real life, we are not always given all the data needed to solve a problem, and we need to research some of the information, particularly values of physical properties.
 
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