Question

During flow over a given body, the drag force, the upstream velocity, and the fluid density are measured. Explain how you would determine the drag coefficient. What area would you use in calculations?

Short answer

Question: Determine the drag coefficient when the drag force, upstream velocity, and fluid density are measured during the flow over a body. Answer: To find the drag coefficient, follow these steps: Step 1: Understand the drag coefficient formula, which is Cd = (2 * Fd) / (ρ * V^2 * A). Step 2: Identify the reference area (A) based on the object's shape. Step 3: Collect the measured data such as drag force (Fd), upstream velocity (V), and fluid density (ρ). Step 4: Calculate the drag coefficient using the formula Cd = (2 * Fd) / (ρ * V^2 * A) by plugging in the values obtained from the measurements and the reference area. Remember, the drag coefficient is a dimensionless quantity that helps in understanding the behavior and performance of a body in a fluid flow.

Step-by-step solution

Understand the drag coefficient formula

The drag coefficient (Cd) is a dimensionless quantity used to quantify the drag or resistance of an object in a fluid environment. It is defined as the ratio of the drag force (Fd) experienced by the body to the dynamic pressure acting on the body. Mathematically, it can be expressed as: Cd = (2 * Fd) / (ρ * V^2 * A) where: Cd = drag coefficient Fd = drag force ρ = fluid density V = upstream velocity A = reference area

Identify the reference area to use in calculations

The reference area (A) is an important parameter in the drag coefficient formula as it is used to normalize the drag force. For different object shapes, the reference area can be different. For example, for a sphere or a cylinder, the reference area is their maximum cross-sectional area. For streamlined bodies like airfoils, the reference area is the planform area (the area that is obtained when the airfoil is projected onto a plane perpendicular to the flow direction).

Collect the required data

Based on the exercise, the following data is measured: - Drag force (Fd) - Upstream velocity (V) - Fluid density (ρ) The reference area (A) must also be determined based on the object's shape, as described in Step 2.

Calculate the drag coefficient

Using the measured data and the reference area, plug the values into the drag coefficient formula to find the drag coefficient: Cd = (2 * Fd) / (ρ * V^2 * A) By following these steps, the drag coefficient for the given body can be determined, which helps in understanding the behaviour and performance of the body in the fluid flow.