Chapter 1.10, Problem 73E

(a)

To determine

To find:the equation for relationship between pressure and depth below the ocean surface.

Answer to Problem 73E

  $\text{P=0}\text{.434h+15}$ .

Explanation of Solution

Given:

  $\text{h=0}$ , $\text{P=15}\text{lb}/{\text{m}}^{\text{2}}$ and $\text{m=}\frac{4.34}{10}$ .

Concept used:

According to straight line formula:

  ${\text{y-y}}_{\text{0}}\text{=m}\left({\text{x-x}}_{\text{0}}\right)$ .

Calculation:

At $\text{h=0}$ , $\text{P=15}\text{lb}/{\text{m}}^{\text{2}}$ and $\text{m=}\frac{4.34}{10}$ .

According to straight line formula:

  ${\text{y-y}}_{\text{0}}\text{=m}\left({\text{x-x}}_{\text{0}}\right)$ .

  $\text{P-15=m}\left(\text{h-0}\right)$ .

  $\text{P-15=}\frac{4.34}{10}\left(\text{h-0}\right)$ .

Hence, equation of pressure is $\text{P=0}\text{.434h+15}$ .

(b)

To determine

To sketch:the graph of the linear equation.

Answer to Problem 73E

The graph is straight line and the graph shows with increasing in depth the water pressure also Increases.

Explanation of Solution

Given:

  $\text{h=0}$ , $\text{P=15}\text{lb}/{\text{m}}^{\text{2}}$ and $\text{m=}\frac{4.34}{10}$ .

Concept used:

The graph can be calculated through Desmos graphing calculator.

Calculation:

The graph the linear equation $\text{P=0}\text{.434h+15}$

  

Here y-axis is pressure and x-axis height or depth.

The graph is straight line and the graph shows with increasing in depth the water pressure also increases.

at $-34.562$ depth water pressure is $0$ .

At 0 height ofdepth the pressure is 15 $\text{lb}/{\text{m}}^{\text{2}}$ .

(c)

To determine

To find:the slope and intercept of y using representation of graph.

Answer to Problem 73E

Slope is rate of increase of pressure with depth, and y intercept is pressure at surface of ocean.

Explanation of Solution

Given:

  $\text{h=0}$ , $\text{P=15}\text{lb}/{\text{m}}^{\text{2}}$ and $\text{m=}\frac{4.34}{10}$ .

Concept used:

According to straight line formula:

  ${\text{y-y}}_{\text{0}}\text{=m}\left({\text{x-x}}_{\text{0}}\right)$ .

m here is slope of the straight line.

Calculation:

Slope is rate of increase of pressure with depth, and y intercept is pressure at surface of ocean.

(d)

To determine

To find:the depth of water when given pressure is $\text{P=100}\text{lb}/{\text{in}}^{\text{2}}$ .

Answer to Problem 73E

Depth of the water is $\text{h=}\frac{\text{85}}{\text{0}\text{.434}}\text{=195}\text{.85ft}$ .

Explanation of Solution

Given: $\text{P=100}\text{lb}/{\text{in}}^{\text{2}}$ .

Concept used:

According to straight line formula:

  ${\text{y-y}}_{\text{0}}\text{=m}\left({\text{x-x}}_{\text{0}}\right)$ .

Calculation:

  $\text{P=100}\text{lb}/{\text{in}}^{\text{2}}$ .

According to straight line formula:

  ${\text{y-y}}_{\text{0}}\text{=m}\left({\text{x-x}}_{\text{0}}\right)$ .

  $\text{100=0}\text{.434h+15}$ .

Depth of the water is $\text{h=}\frac{\text{85}}{\text{0}\text{.434}}\text{=195}\text{.85ft}$ .