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It is proposed to determine the hydrodynamic drag force D on a cable being dragged behind a ship. The cable is assumed to be very long and smooth and is fully submerged and neutrally buoyant (does not sink nor float). An economical way of achieving this is by making small scale experiments in a water tunnel. Basic fluid mechanics tells us that the drag force should be completely determined by the cable's length L and diameter d, the ship's velocity v and the water's density p and viscosity p. a) In your own words, explain how dimensional analysis can be used to translate small scale experimental results to full scale systems like the situation above. b) How many relevant dimensionless groups can be derived for this problem? Explain how you got to this number. c) Using the usual method as seen in this module, show that for the physical problem above, dimensional analysis is consistent with experimental data indicating that the drag force D can be obtained from: D= pvEt Re.

It is proposed to determine the hydrodynamic drag force D on a cable being dragged behind a ship. The cable is assumed to be very long and smooth and is fully submerged and neutrally buoyant (does not sink nor float). An economical way of achieving this is by making small scale experiments in a water tunnel. Basic fluid mechanics tells us that the drag force should be completely determined by the cable's length L and diameter d, the ship's velocity v and the water's density p and viscosity p. a) In your own words, explain how dimensional analysis can be used to translate small scale experimental results to full scale systems like the situation above. b) How many relevant dimensionless groups can be derived for this problem? Explain how you got to this number. c) Using the usual method as seen in this module, show that for the physical problem above, dimensional analysis is consistent with experimental data indicating that the drag force D can be obtained from: D= pvEt Re.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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It is proposed to determine the hydrodynamic drag force D on a cable being dragged behind a ship. The cable is assumed to be very long and smooth and is fully submerged and neutrally buoyant (does not sink nor float). An economical way of achieving this is by making small scale experiments in a water tunnel. Basic fluid mechanics tells us that the drag force should be completely determined by the cable's length L and diameter d, the ship's velocity v and the water's density p and viscosity p. a) In your own words, explain how dimensional analysis can be used to translate small scale experimental results to full scale systems like the situation above. b) How many relevant dimensionless groups can be derived for this problem? Explain how you got to this number. c) Using the usual method as seen in this module, show that for the physical problem above, dimensional analysis is consistent with experimental data indicating that the drag force D can be obtained from: D= pv'L1 Re.
Transcribed Image Text:It is proposed to determine the hydrodynamic drag force D on a cable being dragged behind a ship. The cable is assumed to be very long and smooth and is fully submerged and neutrally buoyant (does not sink nor float). An economical way of achieving this is by making small scale experiments in a water tunnel. Basic fluid mechanics tells us that the drag force should be completely determined by the cable's length L and diameter d, the ship's velocity v and the water's density p and viscosity p. a) In your own words, explain how dimensional analysis can be used to translate small scale experimental results to full scale systems like the situation above. b) How many relevant dimensionless groups can be derived for this problem? Explain how you got to this number. c) Using the usual method as seen in this module, show that for the physical problem above, dimensional analysis is consistent with experimental data indicating that the drag force D can be obtained from: D= pv'L1 Re.
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