Question

A cylindrical object of diameter 900 mm is designed to move axially in air at 60 m/s. Its drag is estimated on a geometrically half-scaled model in water, assuming flow similarity. Co-efficients of dynamic viscosity and densities for air and water are \(1.86 \times 10^{-5}\) Pa-s, 1.2 kg/m\(^3\) and \(1.01 \times 10^{-3}\) Pa-s, 1000 kg/m\(^3\) respectively. Drag measured for the model is 2280 N. Drag experienced by the full-scale object is ___ N (rounded off to the nearest integer).

• A. 322
• B. 644
• C. 1288
• D. 2576

Hint:

For geometrically scaled models, use Reynolds number similarity to estimate drag forces by considering fluid properties, velocities, and characteristic lengths.

Answer 1

The Correct Option is B

Step 1: Use Reynolds number similarity.
For flow similarity, the Reynolds numbers for the model and the full-scale object must be the same. Reynolds number is given by: \[ Re = \frac{\rho v D}{\mu}, \] where \(\rho\) is density, \(v\) is velocity, \(D\) is diameter, and \(\mu\) is dynamic viscosity. Step 2: Apply flow similarity.
For geometrically similar objects, the drag force ratio between the full scale and model is proportional to the Reynolds number ratio. For the model and full-scale object, the drag force \(F_d\) is related to the Reynolds number ratio as: \[ \frac{F_{d,\text{full scale}}}{F_{d,\text{model}}} = \left( \frac{\rho_{\text{full scale}} \cdot v_{\text{full scale}} \cdot D_{\text{full scale}}}{\mu_{\text{full scale}}} \right) \div \left( \frac{\rho_{\text{model}} \cdot v_{\text{model}} \cdot D_{\text{model}}}{\mu_{\text{model}}} \right). \] Using the values provided, we calculate the drag for the full-scale object to be 644 N.