Please use MATLAB to solve the following and include the code written:

Given:

The general formula for terminal velocity is:

We can assume that the velocity v depends on the particles diameter D, the viscosity and the acceleration g. Also, we will assume that the velocity is directly proportional to the difference between the density 1 of the marble and the density 2 of the fluid. And as such, k is the proportionality (dimensionless constant).

Task:

Utilize the data and given information to create a predictive model of terminal velocity so that you may be given a random marble and fluid's dimensions and be able to predict its terminal velocity. This requires tabulation of dimensionless products to reach the solution.

Data:

kDg(P1-P2) v= Marble 1. Mass m = .003 kg, radius r = .0070 m. Marble 2. Mass m = .005 kg, radius r = .0080 m. Marble 3. Mass m = .013 kg, radius r = .0110 m. Marble 4. Mass m = .022 kg, radius r = .0130 m. = = Marble 5. Mass m = .054 kg, radius r = .0175 m. Fluid 1. Kroger Light Corn syrup, density P 1427.1 kg/m, viscosity u 5.0 kg/m/s. Fluid 2. Suave Daily Clarifying Shampoo, density p= 1018.0 kg/m, viscosity u = 20.0 kg/m/s. 3 Table 1: Physical properties of fluids and marbles. Fluid/Marble Marble 1 .026 m/s Shampoo .009 m/s Corn syrup Marble 2 Marble 3 Marble 4 Marble 5 .030 m/s .046 m/s .070 m/s.076 m/s .010 m/s .016 m/s .019 m/s .021 m/s Table 2: Experimental terminal velocities. kDg(P1-P2) v= Marble 1. Mass m = .003 kg, radius r = .0070 m. Marble 2. Mass m = .005 kg, radius r = .0080 m. Marble 3. Mass m = .013 kg, radius r = .0110 m. Marble 4. Mass m = .022 kg, radius r = .0130 m. = = Marble 5. Mass m = .054 kg, radius r = .0175 m. Fluid 1. Kroger Light Corn syrup, density P 1427.1 kg/m, viscosity u 5.0 kg/m/s. Fluid 2. Suave Daily Clarifying Shampoo, density p= 1018.0 kg/m, viscosity u = 20.0 kg/m/s. 3 Table 1: Physical properties of fluids and marbles. Fluid/Marble Marble 1 .026 m/s Shampoo .009 m/s Corn syrup Marble 2 Marble 3 Marble 4 Marble 5 .030 m/s .046 m/s .070 m/s.076 m/s .010 m/s .016 m/s .019 m/s .021 m/s Table 2: Experimental terminal velocities