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# fluids02 - then determine ¢ p j real from ¢ p j model The...

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When a capillary tube is lowered into a liquid and then withdrawn, the meniscus of the °uid is at a height ¢ h above the liquid surface. It is found experimentally that ¢ h depends upon the tube diameter D , the liquid's surface tension ¾ , and the liquid's speci¯c weight ½g . Write an expression for the functional dependence of ¢ h in terms of the dimensionless parameters of the problem.

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Oil °ows at V = 1 m/s along a section of the Alaska pipeline that is ` = 10 miles long and 2 m in diameter, with a density ½ = 900 kg/m 3 and a kinematic viscosity of º = 0 : 002 m 2 /s. The pressure drop ¢ p over the 10 miles of pipe is known to depend on ½ , V , ¹ , ` and D . The pressure is to be predicted by carrying out a scale experiment using water and a pipe of 5 mm diameter. What length of pipe is required, and at what velocity must the water °ow? How would you
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Unformatted text preview: then determine ¢ p j real from ¢ p j model ? The propellor of a 150 m long cargo ship is 2.5 m in diameter and rotates at 100 rpm under normal operating conditions. A 1:100 scale model of the ship and its propellor is to be tested in a towing tank to ¯nd the drag force on the ship that the propellor must overcome. It is known that °ows near free surfaces depend on g , whereas e®ects of water viscosity on this °ow can be neglected. 1. Which dimensionless groups must be matched to ensure dynamic similarity? 2. At what rpm should the model propellor rotate? 3. If the drag coe±cients of the model and the full-size ship are the same, what is the ratio of power expended by each?...
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fluids02 - then determine ¢ p j real from ¢ p j model The...

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