6. Find the circulation and outward flux of the velocity field = sin yi + cos y) over the square cut from the first quadrant by the lines and y = .
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- A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v = (x - y, z + y + 6, z? ) and the net is decribed by the equation y = 1 – x - z', y 2 0, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.) · dS = IncorrectSuppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 5x² - 3xy + xyz (a) Find the rate of change of the potential at P(5, 2, 5) in the direction of the vector v = i + j - k. (b) In which direction does V change most rapidly at P? 73°F Mostly cloudy (c) What is the maximum rate of change at P? Need Help? Read It Show My Work (Optional)? Watch It Q6) Let f(xxx)=3xy²-x² be a potential function of a fluid velocity field. a) Find the magnitude of the greatest rate of change for f(x,y) at (1,3). Please provide a physical interpretation. b) Find the direction angles for this greatest rate of change. Express angles in degrees. Please provide a physical interpretation.
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