Question

A cone is partially immersed in moving water. The cone experiences a lift force F (see below). Mr. John Doe was asked to build a 1/10 scale model of the original cone and use it to predict the life force on the original cone. John’s boss told him that F depends on water’s volumetric flowrate Q, water density , the gravity g, the cone angle , and the cone’s immersion diameter, D.

(1) Perform a dimensional analysis for this problem. Hints:  is dimensionless and a good choice of the repeating variables is g, and D.

Problem 3 [30 points]: A cone is partially immersed in moving water. The cone experiences a lift force F (see below). Mr. John Doe was asked to build a 1/10 scale model of the original cone and use it to predict the life force on the original cone. John's boss told him that F depends on water's volumetric flowrate Q, water density p, the gravity g, the cone angle 0, and the cone's immersion diameter, D. (1) Perform a dimensional analysis for this problem. Hints: 0 is dimensionless and a good choice of the repeating variables is p, g, and D. [15 points] (2) If the flowrate passing the original cone is 30 m/s, determine the flowrate must be used when testing the model. The model was run under normal gravity in water. [5 points] (3) If the model force is 10N, help John predict the force felt by the original cone. [5 points] (4) Later, the lift force felt by the original cone was found to be 30% higher than your prediction. John checked the model and his experiments, but found no flaws. What could have caused your prediction to be off? [5 points] VIIIII IIIIIIIIIIIIIIIIII Il

(2) If the flowrate passing the original cone is 30 m3/s, determine the flowrate must be used when testing the model. The model was run under normal gravity in water.

(3) If the model force is 10N, help John predict the force felt by the original cone.

(4) Later, the lift force felt by the original cone was found to be 30% higher than your prediction. John checked the model and his experiments, but found no flaws. What could have caused your prediction to be off?

Answer 1

As, - density of water g' in also same in nad changing & for both hence, Finland - 10x103 = 10" N Any Ang As Lift force felt by the original cone was found to be 30% higher than prediction because here only gravity force in considered as marjor force & other forces which is acting sici friction or riscous force pressure force, & surface tensian force which is ignored here,