Smartbook #7
The required ratio of kinematic viscosities to match both Reynolds number and Froude number for the case of flows with free surfaces is νmνpν�ν� = (LmLp����)3/2 If LmLp���� = 110110, υm would be υp, which is very unrealistic to achieve. (Round the answer to three decimal places)
0.03
Calculate speed (Vm) for the model car, if the velocity of the prototype (Vp) is 28.8 m/s, the ratio of the coefficient of viscosity of model to prototype μmμpμ�μ� is 1, the ratio of density of prototype to density of model ρpρmρ�ρ� is 1, and the ratio of length of prototype to length of model LpLm���� is 16
461 m/s
Consider a problem in which there are five original parameters (one of which is a dependent parameter). Assuming that three primary dimensions are represented in the problem, after conducting a dimensional analysis for the same resolution (five tested levels of each independent parameter), a total of _____ experiments need to be conducted. 125 5 625 25
5
Consider a problem in which there are five original parameters (one of which is a dependent parameter). A complete set of experiments is conducted by testing every possible combination of several levels of each of the four independent parameters. A full factorial test with five levels of each of the four independent parameters would require _____ experiments.
625
There are _____ primary dimensions. seven five three two
7
_____ are defined as dimensional quantities that change or vary in the problem. Nondimensional variables Parameters Dimensional constant Dimensional variables
Dimensional variables
Identify the units of length from the following. (Check all that apply.) Newton Feet Pound-mass Micron
Feet Micron
Force-scale factor < 1
Force on the model is less than that on the prototype.
Force-scale factor > 1
Force on the model is more than that on the prototype.
Identify the true statements about a distorted model when testing flows are rivers and dams. (Check all that apply.) . It is a model in which the vertical scale of the model is exaggerated in comparison to the horizontal scale of the model. The model riverbed slope is often made proportionally steeper than that of the prototype. It is a model in which the horizontal scale of the model is exaggerated in comparison to the vertical scale of the model. The prototype riverbed slope is often made proportionally steeper than that of the model.
It is a model in which the vertical scale of the model is exaggerated in comparison to the horizontal scale of the model. The model riverbed slope is often made proportionally steeper than that of the prototype.
Identify the components of total energy of a system. (Check all that apply.) Kinetic energy External energy Potential energy Internal energy
Kinetic energy Potential energy Internal energy
Identify the law that states that every additive term in an equation must have the same dimensions.
Law of dimensional homogeneity
Geometric scale factor > 1
Model larger than prototype
Geometric scale factor < 1
Model smaller than prototype
Identify the parameters that need to be matched for complete similarity between model and prototype for the case of flows with free surfaces. (Check all that apply.) Biot number Euler's number Reynolds number Froude number
Reynolds number Froude number
Identify the definitions of Reynolds number (Re). (Check all that apply.) The ratio of speed of an object moving through a fluid and the local speed of sound The ratio of characteristic speed and length to kinematic viscosity the ratio of density, characteristic speed, and characteristic length to dynamic viscosity. The ratio of kinematic viscosity to thermal diffusivity
The ratio of characteristic speed and length to kinematic viscosity the ratio of density, characteristic speed, and characteristic length to dynamic viscosity.
Identify the primary dimensions that are used to express the three components of total energy of a system, that is, internal energy, kinetic energy, and potential energy. Time (t) Mass (m) Length (L) Velocity (V)
Time (t) Mass (m) Length (L)
Identify the options that can be used to match the model Reynolds number to that of the prototype in a flow facility such as a wind tunnel for a situation in which the maximum Reynolds number of the model is too small compared to that of the prototype. (Check all that apply.) We could use a different fluid for the model tests. We could lower the pressure in the wind tunnel to increase the Reynolds number. If we had a bigger wind tunnel, we could test with a larger model. We could run the wind tunnel at several speeds near the maximum speed and extrapolate the results.
We could use a different fluid for the model tests. If we had a bigger wind tunnel, we could test with a larger model. We could run the wind tunnel at several speeds near the maximum speed and extrapolate the results.
The powerful technique that is introduced to properly scale model performance to prototype performance to is called _____ analysis
dimensional
d2zdt2�2�dt2 = -g g in the given equation is a _____.
dimensional constant
d2zdt2�2�dt2 = -g z and t in the given equation are _____.
dimensional variables
For the case of model testing of water flows with free surfaces in which complete similarity cannot be achieved, a _____ model is often used. geometrically similar wind tunnel prototype distorted
distorted
n most experiments, to save time and money, tests are performed on a geometrically scaled ___ , rather than on the full-scale prototype.
model
Angle of rotation measured in degrees or radians
nondimensional variable
π and e in certain equations as a result of integration are called _____.
pure constants
In the case of aerodynamic drag on an automobile, the flow is approximated as incompressible and is given by Π1=f(Π2), where Π1 is a nonstandard form of the drag coefficient and Π2 is the Reynolds number. Identify Π1 and Π2. Π1= FDρV2L2FDρV2L2; Π2= ρVLμρVLμ Π1=ρVLμρVLμ; Π2= FDρV2L2FDρV2L2 Π1= ρV3L2FDρV3L2FD; Π2= μρVLμρVL Π1= μρVLμρVL; Π2=ρV2LFD
Π1= FDρV2L2FDρV2L2; Π2= ρVLμ
Identify the pure constants from the following. (Check all that apply.) L π e g
π e
