Chapter 1.5, Problem 7P

Solution

To find: The wind speed that produces a required pressure.

The pressure of $P\text{=30}\text{lb}\text{./f}{\text{t}}^{\text{2}}$ is produced by the wind of speed 108.253 miles/hour.

Given data:

The pressure P (lb. /ft²) from wind blowing at s miles per hour is given by $P=\left(0.00256\right)s^2$ . The required wind speed is that produces pressure of $\text{30}\text{lb}\text{./f}{\text{t}}^{\text{2}}$ , i.e., $P\text{=30}\text{lb}\text{./f}{\text{t}}^{\text{2}},s\text{=?}$ .

Method/Formula used:

The graph of function P is drawn using graphing utility taking pressure on vertical axis and speed of wind on horizontal axis.

Calculations/Graph:

The relation between pressure and velocity is $P=\left(0.00256\right)s^2$ that can be written as,

  $P=\left(0.00256\right)s^2$ .

The graph of function $P=\left(0.00256\right)s^2$ is shown in Fig. (1).

  

From the graph it is clear that corresponding to $P=30$ there exists a point $x=108.253$ on the graph of the function $P=\left(0.00256\right)s^2$ . That shows the pressure of $P\text{=30}\text{lb}\text{./f}{\text{t}}^{\text{2}}$ is produced by the wind of speed 108.253 miles/hour.