A square parking lot of width w is bounded on all sides by a curb of height d with only...

A square parking lot of width w is bounded on all sides by a curb of height d with only one opening of width b as shown in Fig. P7.57. During a heavy rain the lot fills with water and it is of interest to determine the time, t, it takes for the water to completely drain from the lot after the rain stops. A scale model is to be used to study this problem, and it is assumed that

where g is the acceleration of gravity, μ is the fluid viscosity, and ρ is the fluid density. (a) A dimensional analysis indicates that two important dimensionless parameters are b/w and d/w. What additional dimensionless parameters are required? (b) For a geometrically similar model having a length scale of 1/10, what is the relationship between the drain time for the model and the corresponding drain time for the actual parking lot? Assume all similarity requirements are satisfied. Can water be used as the model fluid? Explain and justify your answer.