Question

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° 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

Answer 1

The flows can be classified as one-, two-, or three-dimensional. Rainwater flow down a wide driveway can be classified as two-dimensional with streamlines flowing downwards in parallel lines.

Step-by-step explanation:

(a) Rainwater flow down a wide driveway: This flow can be classified as two-dimensional. Streamlines would be parallel lines flowing downwards.

(b) Flow in a straight horizontal pipe: This flow can be classified as one-dimensional. Streamlines would be straight lines along the length of the pipe.

(c) Flow in a straight pipe inclined upward at a 45° angle: This flow can be classified as two-dimensional. Streamlines would be inclined lines flowing upwards.

(d) Flow in a long pipe that follows the ground in hilly country: This flow can be classified as three-dimensional. Streamlines would follow the contours of the ground.

(e) Flow over an airplane: This flow can be classified as three-dimensional. Streamlines would follow the shape of the airplane and its wings.

(f) Wind blowing past a tall telephone: This flow can be classified as three-dimensional. Streamlines would follow the shape of the telephone and its surroundings.

(g) Flow in the impeller of a centrifugal pump: This flow can be classified as three-dimensional. Streamlines would follow the shape of the impeller and its rotation direction.