Vector Field Problem: Pressure Tendency at Service Station

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SUMMARY

The discussion focuses on solving a vector field problem related to pressure tendency at a service station, where a car travels southward at 100 km/h. The surface pressure decreases toward the southeast at a rate of 1 Pa/km, while the pressure measured by the car decreases at 50 Pa/3h. Participants emphasize the need to utilize the advection equation, which involves the divergence of the velocity gradient, to determine the pressure tendency accurately. The conversation highlights the challenge of relating given information to the appropriate mathematical forms for gradient fields.

PREREQUISITES
  • Understanding of vector fields and gradient fields
  • Familiarity with the advection equation and its application
  • Knowledge of divergence in vector calculus
  • Ability to interpret physical concepts in mathematical terms
NEXT STEPS
  • Study the advection equation in detail, focusing on its derivation and applications
  • Learn how to compute the divergence of vector fields using specific examples
  • Explore gradient fields and their representation in mathematical notation
  • Practice solving problems involving pressure tendency and vector fields in fluid dynamics
USEFUL FOR

Students in physics or engineering, particularly those studying fluid dynamics, vector calculus, or anyone tackling problems involving pressure changes in moving fluids.

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Homework Statement


A car is driving straight southward, past a service station, at 100 km/h. The surface pressure decreaes toward the southeast at 1 Pa/km. What is the pressure tendency at the service station if the pressure measured by the car is decreasing at a rate of 50 Pa/3h? (Hint: draw a vector diagram to make sure you get the directions correct and use the advection equation).

Homework Equations



Advection equation is the divergence of the velocity gradient

The Attempt at a Solution


Im having some trouble understanding some concepts with gradient fields. The ultimate goal is to add two gradient fields and then take the divergence I think.

All the divergence problems I have looked at already have the equation given in the form of f(x,y,z) or F(x,y,z)=xyzi + xyzj + xyzk. I think I want to find an equation of the 2nd form. I don't understand how to relate the information I was given into that form.

I think the equation for the gradient going in the -y direction would be F(x,y,z) = 0i-.1667yj+0k. I don't understand how to get the second equation with the y=-x format. Then do I just add the components to get the full vector field? And then take the divergence of the added fields?

Thanks much.
 
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Hi, I have this same question and have know idea how to set up the advection equation. Please help!
 

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