这个作业是完成数学建模相关的计量模型题目
Math 370 – Mathematical Modeling
1.确定以下等式在尺寸上是否正确？ （10分）
2.尺寸分析：假设V，液体的速度
流经水平管，取决于压力
下降∆P，管道长度l，直径D，密度
液体ρ的粘度和液体μ的粘度。 节目
V可以用白金汉Π定理建模
如
（）。 2
2
μ
ρ
ρ
微米
升
d
d
V ∆ =⋅Φ（10分）
3.相似性：假设旋转直径为D（cm）的圆盘浸入水中时所需的扭矩τ（N m）。
密度ρ（kg / m3
），并且在转速ω（弧度/ s）下的堆积粘度ν（kg / m / s）可以
用白金汉姆定理作为模型，
If a scaled model, 50 times smaller, experiences a 5 N-m torque in water with the rotation rate
10 sec
3π rad
ω = and
the real-sized model is tested in oil. Assuming the two models are similar and water kinematic viscosity = 1.2
oil kinematic viscosity and water density = 3 oil density,
a) What is the rotation rate for the real-size model? (5 points)
b) At that rotation rate, what is the real-sized torque? (5 points)
4) Modeling with data: Given the data set populations versus the mean velocities over a 50-foot course for
15 locations on Table 4.5 of page138, find two non-polynomial models that can describe the relation between
P and V with 𝑅𝑅2 ≥ 92%. For each model, provided the mathematical equation with the parameters specified
along with the graph. You must include the R-square values. (10 pts for each model)