Classify the following flows as one- , two-, or three-dimensional. Sketch a few streamlines for each. (a) Rainwater flow down a wide driveway (b) Flow in a straight horizontal pipe (c) Flow in a straight pipe inclined upward at a \(45^{\circ}\) angle (d) Flow in a long pipe that follows the ground in hilly country (e) Flow over an airplane (f) Wind blowing past a tall telephone (g) Flow in the impeller of a centrifugal pump

(a) Rainwater flow down a wide driveway is two-dimensional. The water flows downwards and sideways along the width of the driveway, but not significantly in the third dimension (across the depth of the driveway).(b) Flow in a straight horizontal pipe is one-dimensional. This is because the fluid flows in only one direction—along the length of the pipe.(c) Flow in a straight pipe inclined upward at a \(45^{\circ}\) angle can be classified as one-dimensional because the fluid predominantly flows along the axis of the pipe.(d) Flow in a long pipe that follows the ground in hilly country can be considered one-dimensional. Even though the pipe follows the contours of the land, the flow is mainly guided along the axis of the pipe.(e) Flow over an airplane is three-dimensional. The fluid (air) flows over the length, width and height of the airplane.(f) Wind blowing past a tall telephone is three-dimensional. The wind can stream around the pole in all directions—upward, horizontal and cross-wise.(g) Flow in the impeller of a centrifugal pump is three-dimensional because the fluid is moved radially outward in all directions.