Question

Solve and Discuss Concept Problem

The drag, F D on a thin rectangular plate ( $LaTeX: l\times h$ l × h in size) placed normal to a fluid with velocity V, is a function of the following variables:

$LaTeX: F_D=f\left(l,\:h,\:V,\:\mu,\:\rho\right)$ F D = f ( l , h , V , μ , ρ )

1. Find the dimensionless groups formed as $LaTeX: \prod_1=\Phi\left(\prod_2,\:\prod_3\right)$ ∏ 1 = Φ ( ∏ 2 , ∏ 3 ). Do not show your solution but only the final Pi-terms.
2. A prototype billboard is going to be built in your city, and you need to design a test model to study the drag at different climate condition on this billboard. Write the similarity requirements using the Pi-terms found in part (a), and determine the required fluid velocity for your test model.
   Hint: Start with estimation of the prototype billboard dimensions $LaTeX: \left(l\times h\right)$ ( l × h ) with your common sense (you can use an existing billboard in your city as a reference), and find the average wind speed in your city from a credible resource (cite the resource).
3. Discuss your findings with your classmates.

Answer 1

sariables. following var As we know, & Drag force depends upon • Dimensions of the body fluid velocity o fluid viscosity o fluid Density Foi f ( 1 , b, V, W,P)

Now to perform the dimensional analysis using pi - Theorm, One needs to select the dependent and independent Variables. Thus forming a functional relation among the variables. In the given problem we have fo, 1 k v, R, S = 6 Variables hence selecting T Variade; We know h&l. [LI : ve [LT-1] = [METY po{MERJ fo- [MLT2)

We have; 3 represent the to T terms relation; T T and T = $(A. Tz) Selecting pinil as the Variables we get Ta Now, coming back to the application. The similarity requirme Geometric kinematic Dynamic

first one will be achieved by the term h by the size and shape of the model and the proto type. [lol lm- in geometric Scale] 2. Kinematic similarity : numbe Rp, Reynold Member (13) ie: ) ne ( ) ( cu entong V 1 Model

Dynamic Similarity (por me puhi or model pul / Protopype je to 4150 (Co) model - (Co) prototype To obtain the velocity of the model tests; from the Kine matic Similitude;

where de la und