Vector Field Problem: Pressure Tendency at Service Station

In summary, the conversation discusses the use of the advection equation to determine the pressure tendency at a service station as a car drives southward at 100 km/h. The surface pressure is decreasing toward the southeast at a rate of 1 Pa/km, while the car measures a decrease of 50 Pa/3h. The conversation also mentions the use of gradient fields and the need to add two gradient fields and take the divergence to solve the problem.
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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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  • #2
Hi, I have this same question and have know idea how to set up the advection equation. Please help!
 

1. What is a vector field problem?

A vector field problem is a mathematical problem that involves the analysis and prediction of the behavior of a vector field. A vector field is a mathematical concept that describes the magnitude and direction of a physical quantity, such as wind speed or pressure, at every point in a given space. In the context of a service station, a vector field problem may involve analyzing the pressure tendencies of the air around the station.

2. What is pressure tendency?

Pressure tendency refers to the change in atmospheric pressure over a given period of time. It is often represented as a vector, with both magnitude and direction. A positive pressure tendency indicates an increase in pressure, while a negative pressure tendency indicates a decrease in pressure. In the context of a service station, understanding pressure tendency can help predict changes in weather patterns and potential impacts on gas prices.

3. How is pressure tendency measured at a service station?

Pressure tendency at a service station can be measured using various instruments, such as barometers or anemometers. These instruments measure changes in atmospheric pressure and wind speed, respectively. Data from these instruments can be analyzed to determine the pressure tendency at the service station.

4. What factors can affect pressure tendency at a service station?

There are several factors that can affect pressure tendency at a service station, including changes in weather patterns, altitude, temperature, and proximity to other physical structures. For example, a service station located in a low-pressure system may experience a decrease in pressure, while a station located at a higher altitude may experience a different pressure tendency due to changes in air density. Other factors, such as wind speed and direction, can also impact pressure tendency at a service station.

5. How can understanding pressure tendency at a service station be useful?

Understanding pressure tendency at a service station can be useful for a variety of reasons. It can help predict changes in weather patterns, which can impact gas prices and the demand for fuel. It can also inform decisions about when to adjust tire pressure for optimal fuel efficiency, as well as help with maintenance and safety measures related to changes in atmospheric pressure. Additionally, understanding pressure tendency can aid in the overall management and operation of a service station.

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