Analyzing Airflow Patterns in Your Apartment

You recently moved into a small apartment and noticed that some areas feel stuffy while others have a nice breeze when your window fan is running. Curious about the airflow patterns, you borrow a handheld anemometer from a friend in the engineering program to measure air velocity at different points in your rectangular living space. The room measures [latex]4[/latex] meters by [latex]3[/latex] meters. Based on your measurements, you model the air velocity as a vector field [latex]\mathbf{F}(x,y) = \langle P(x,y), Q(x,y) \rangle[/latex] where [latex]x[/latex] and [latex]y[/latex] are positions in meters and the components are in meters per second. You want to understand how air circulates around the room and how much air flows across certain boundaries. This information will help you decide where to place a second fan or reposition furniture for better airflow.