Chapter 10, Problem 1ICA

ICA 10-5

The worksheet shown here was designed to calculate the total pressure felt by an object submerged in a fluid as a function of the depth to which the object is submerged. The user will enter the surface pressure (in units of atmospheres), specific gravity of the fluid, and the gravity of the planet (in units of meters per second squared). All user input is shown in red. The worksheet will calculate the surface pressure in units of pascals, the density of the fluid in kilograms per cubic meter, and depth in units of feet. All conversions are shown in orange. Finally, the worksheet will calculate the total pressure in units of atmospheres.

1. a. What formula should be typed in cell C8 to convert the surface pressure in cell C4 from atmospheres to pascals?
2. b. What formula should be typed in cell C9 to determine the density in units of kilograms per cubic meter?
3. c. What formula should be typed into cell B12 that can then be copied clown column B to convert the depth from units of feet to units of meters?
4. d. What formula should be typed into cell C12 that can then be copied down column C to calculate the total pressure in units of atmospheres?

To determine

Write the formula to be entered in cell C8 to convert the atmospheres surface pressure entered in cell C4 to Pascal.

Answer to Problem 1ICA

The formula to be entered in cell C8 to convert the atmospheres surface pressure entered in cell C4 to Pascal is “$\underset{\_}{=\text{C}4*101325}$”.

Explanation of Solution

Given data:

The worksheet is given as follows.

Calculation:

Consider the conversion factor for atmospheres to Pascal.

$1\text{atmosphere}=101,325\text{pascal}$ (1)

Step 1:

Using equation (1), enter the formula “$=\text{C}4\ast 101,325$” in cell C8 to convert the atmospheres surface pressure entered in cell C4 to Pascal as shown in Figure 1.

Conclusion:

Hence, the formula to be entered in cell C8 to convert the atmospheres surface pressure entered in cell C4 to Pascal is “$\underset{\_}{=\text{C}4*101325}$”.

To determine

Write the formula to be entered in cell C9 to determine the density in units of kilograms per cubic meter.

Answer to Problem 1ICA

The formula to be entered in cell C9 to determine the density in units of kilograms per cubic meter is “$\underset{\_}{=\text{C5}*1000}$”.

Explanation of Solution

Calculation:

Write the expression for density.

$\text{density}=\left(\text{specific gravity}\times \text{1000}\right)\text{kg}/{\text{m}}^3$ (2)

Step 1:

Using equation (2), enter the formula “$=\text{C5}\ast 1,000$” in cell C9 to determine the density in units of kilograms per cubic meter as shown in Figure 2.

Conclusion:

Hence, the formula to be entered in cell C9 to determine the density in units of kilograms per cubic meter is “$\underset{\_}{=\text{C5}*1000}$”.

To determine

Write the formula to be entered in cell B12 that can be then be copied down column B to convert the depth in feet to meters.

Answer to Problem 1ICA

The formula to be entered in cell B12 that can be then be copied down column B to convert the depth in feet to meters is “$\underset{\_}{=\text{A12}\ast \text{0}\text{.3048}}$”.

Explanation of Solution

Calculation:

Write the conversion factor for feet to meter.

$1\text{ft}=0.3048\text{m}$ (3)

Step 1:

Using equation (3), enter the formula “$=\text{A12}\ast 0.3048$” in cell B12 that can be then be copied down column B to convert the depth in feet to meters as shown in Figure 3.

Drag the same formula for remaining cells in the column to obtain the value of depth in terms of m as shown in Figure 4.

Conclusion:

Hence, the formula to be entered in cell B12 that can be then be copied down column B to convert the depth in feet to meters is “$\underset{\_}{=\text{A12}\ast \text{0}\text{.3048}}$”.

To determine

Write the formula to be entered in cell C12 that can be then be copied down column C to calculate the total pressure in atmospheres.

Answer to Problem 1ICA

The formula to be entered in cell C12 that can be then be copied down column C to calculate the total pressure in atmospheres is “$\underset{\_}{=\left(\$\text{C}\$8+\$\text{C}\$9*\$\text{C\$6}\ast \text{B}12\right)/101325}$” or “$\underset{\_}{=\$\text{C}\$4+\left(\$\text{C}\$9*\$\text{C\$6}\ast \text{B}12\right)/101325}$”.

Explanation of Solution

Calculation:

Write the expression for total pressure.

$\text{Total pressure}=\text{Psurface}+\rho gh$ (4)

Re-arrange equation (1) as follows.

$1\text{pascal}=\frac{1}{101,325}\text{atmosphere}$ (5)

Step 1:

Since, the content of cell C8 is in Pascal, the result obtained for total pressure using cell C8, C9, C6 and B12 is divided by 101,325 to convert the result from Pascal to atmosphere.

Using equation (4) and (5), enter the formula “$=\left(\$\text{C}\$8+\$\text{C}\$9*\$\text{C\$6}\ast \text{B}12\right)/101325$” in cell C12 that can be then be copied down column C to calculate the total pressure as shown in Figure 5 and Figure 6.

Drag the same formula for remaining cells in the column to obtain the total pressure value as shown in Figure 6.

Since, the content of cell C4 is in atmosphere, the result obtained for $\rho \text{gh}$ (that is using C9, C6 and B12) is divided by 101,325 and add with cell C4 to obtain total pressure in atmosphere.

Using equation (4) and (5), enter the formula “$=\$\text{C}\$4+\left(\$\text{C}\$9*\$\text{C\$6}\ast \text{B}12\right)/101325$” in cell C12 that can be then be copied down column C to calculate the total pressure as shown in Figure 7.

Drag the same formula for remaining cells in the column to obtain the total pressure value as shown in Figure 8.

Compare Figure 5 with Figure 7 and Figure 6 with Figure 8, the result obtained for total pressure using formula $=\left(\$\text{C}\$8+\$\text{C}\$9*\$\text{C\$6}\ast \text{B}12\right)/101325$ or $=\$\text{C}\$4+\left(\$\text{C}\$9*\$\text{C\$6}\ast \text{B}12\right)/101325$ is same.

Conclusion:

Hence, the formula to be entered in cell C12 that can be then be copied down column C to calculate the total pressure in atmospheres is “$\underset{\_}{=\left(\$\text{C}\$8+\$\text{C}\$9*\$\text{C\$6}\ast \text{B}12\right)/101325}$” or “$\underset{\_}{=\$\text{C}\$4+\left(\$\text{C}\$9*\$\text{C\$6}\ast \text{B}12\right)/101325}$”.