Question

measurements of drag force are made on a model automobile in a towing tank filled with fresh water. the model length scale is 1/5 that of the prototype. state the conditions required to ensure dynamic similarity between the model and the prototype. determine the fraction of the prototype speed in air at which the model test should be made in water to ensure dynamically similar conditions. measurements made at various speeds show that the dimensionless force ratio becomes constant at model test speeds above 4 m/s. the drag force measured during a test at this speed is 182 n. calculate the drag force expected on the prototype vehicle operating at 90 km/hr in air.

Answer 1

To ensure dynamic similarity between the model and the prototype, the model test should be made in water at a fraction of the prototype speed. The fraction can be determined by maintaining the same dimensionless force ratio. Based on the given information, the drag force expected on the prototype vehicle operating at 90 km/hr in air is approximately 1137.5 N.

To ensure dynamic similarity between the model automobile and the prototype, the following conditions need to be met:

1. Geometric similarity: The model length scale is given as 1/5 that of the prototype. This means that the model should maintain the same proportions and shape as the prototype, but at a smaller size.

2. Kinematic similarity: The speeds of the model and the prototype need to be in proportion to their sizes. This can be achieved by maintaining the same dimensionless force ratio at equivalent speeds for both the model and the prototype.

To determine the fraction of the prototype speed in air at which the model test should be made in water, we use the information provided. The dimensionless force ratio becomes constant at model test speeds above 4 m/s. This means that the drag force experienced by the model is proportional to the drag force experienced by the prototype.

Given that the drag force measured during a test at 4 m/s for the model is 182 N, we can use this information to find the expected drag force on the prototype vehicle operating at 90 km/hr in air.

First, we need to convert the prototype speed from km/hr to m/s:

90 km/hr = (90 km/hr) * (1000 m/km) * (1 hr/3600 s) = 25 m/s

Since the dimensionless force ratio is constant, the ratio of the drag forces for the model and prototype should be the same:

Drag force of the model / Drag force of the prototype = 182 N / X (unknown drag force of the prototype)

Using this ratio, we can set up the equation:

182 N / X = 4 m/s / 25 m/s

Simplifying the equation, we find:

X = (182 N * 25 m/s) / 4 m/s = 1137.5 N

Therefore, the drag force expected on the prototype vehicle operating at 90 km/hr in air is approximately 1137.5 N.