- 1 If In A Given Problem There Are N Variables And M Dimensions How Many Repeating Variables Should Be Chosen 2 The 1 (142.09 KiB) Viewed 46 times
- 1 If In A Given Problem There Are N Variables And M Dimensions How Many Repeating Variables Should Be Chosen 2 The 2 (83.94 KiB) Viewed 46 times
1. If in a given problem, there are N variables and M dimensions, how many repeating variables should be chosen? 2. The lift force FL on a wing is dependent on six (6) parameters: the fluid speed V, the chord length Lc, the fluid density p, the fluid viscosity , the , speed of sound c in the fluid, and the angle of attack a of the wing. How many dimensionless products or 1-groups can be formed? 3. The lift force FL on a wing is dependent on six (6) parameters: the fluid speed V, the chord length Lc, the fluid density p, the fluid viscosity , the speed of sound c in the fluid, and the angle of attack a of the wing. Which of the following sets of variables are most appropriate to be chosen as the repeating variables? a. V, Lc, and p b. FL, V, and p c. V and p only d. V, c, and L. 4. The pipe wall shear stress tw is dependent on the average velocity on the pipe V, the fluid density p, the fluid viscosity u, the pipe diameter D, and roughness height ε along the wall of the pipe. Which of the following sets of variables are most appropriate to be chosen as the repeating variables? a. V, D, and p b. D, V, and tw c. , p, and tw d. p and V only 5. Which criterion for dynamic similarity is the most appropriate to be used in models where pressure force is important? a. Euler Criterion b. Reynolds Criterion c. Weber Criterion d. Mach Criterion
6. Which of the following relationships between prototype and model ratios is FALSE for free-surface flows where the Froud criterion governs? Assume that the acceleration due to gravity and the fluid density for both the model and prototype is the same. = a. Q, = L, 3/2 12 b. F, = 4,3 c. P, = L; d. t; = L, 7. A dam spillway is to be tested with a 1:30 scale model. If the model volume flow is 0.05 cms, what will the volume flow of the prototype be? Round off your answer to the nearest tens. 8. To match the Reynolds number in an air flow (vair = 1.51x105 m² /s) and a water flow (Vwater = 1.00x106 m² /s) using the same size model, the velocity in the air flow model should be times higher than the flow in the water flow model. Round off your answer to the nearest whole number.