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).
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 dont 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?