Chapter 15, Problem 2P

To determine

Use MATLAB to create a Table and plot the relationship between height of the water above ground in the water tower and water pressure in pipeline at the base of the tower and also find the height of the water tower when the pressure $80\text{psi}$ is created.

Answer to Problem 2P

The height of the water tower is approximately just below $19\text{0}\text{ft}$ when the pressure $80\text{psi}$ is created.

Explanation of Solution

Given info:

The relationship between the pressure and height is given by,

$P=\rho gh$ (1)

Here,

$P$ is the water pressure at the base of water in $\frac{\text{lb}}{{\text{ft}}^{\text{2}}}$,

$\rho$ is the density of water in $\frac{\text{slugs}}{{\text{ft}}^{\text{3}}}$,

$g$ is the acceleration due to gravity in $\frac{\text{ft}}{{\text{s}}^{\text{2}}}$,

$h$ is the altitude in $\text{ft}$.

$\begin{array}{l}\rho =1.94\frac{\text{slugs}}{{\text{ft}}^{\text{3}}}\\ g=32.2\frac{\text{ft}}{{\text{s}}^{\text{2}}}\end{array}$

Calculation:

The steps to create the table and plot which shows the relationship between height and pressure in MATLAB are as follows,

• Generate a range of values for the height by an increment of $\text{10}\text{ft}$ to find the pressure at different height.
• Use the values of density and acceleration gravity in equation (1) to find the value of pressure.
• To find the value of pressure in $\frac{\text{lb}}{{\text{in}}^{\text{2}}}$ divide the equation (1) by $\text{144}$.
• To print the value of pressure at the 2 decimal digit use “format bank” command.
• Print the value of pressure for the range of height from $\text{0}\text{to}\text{200}\text{ft}$ by an increment of $\text{10}\text{ft}$.

In the MATLAB script editor type the code as follows and save with a name of “unitconversion” as .m file, then execute the code to create the table and plot between height and pressure,

h=0:5:200;

P=(1.94)*(32.2)*(1/144)*h;

format bank

fprintf('\n-------------------------------------')

fprintf('\n\t\th(ft)\t\t\tP(lb/in^2)')

fprintf('\n--------------------------------------\n')

disp([h', P'])

fprintf('----------------------------------------')

plot(h,p)

xlabel('Height (m) ')

ylabel('Pressure (lb/in^2) ')

In the MATLAB command window the result will be displayed as follows,

-------------------------------------

h(ft)P(lb/in^2)

--------------------------------------

             0             0

          5.00          2.17

         10.00          4.34

         15.00          6.51

         20.00          8.68

         25.00         10.85

         30.00         13.01

         35.00         15.18

         40.00         17.35

         45.00         19.52

         50.00         21.69

         55.00         23.86

         60.00         26.03

         65.00         28.20

         70.00         30.37

         75.00         32.54

         80.00         34.70

         85.00         36.87

         90.00         39.04

         95.00         41.21

        100.00         43.38

        105.00         45.55

        110.00         47.72

        115.00         49.89

        120.00         52.06

        125.00         54.23

        130.00         56.39

        135.00         58.56

        140.00         60.73

        145.00         62.90

        150.00         65.07

        155.00         67.24

        160.00         69.41

        165.00         71.58

        170.00         73.75

        175.00         75.92

        180.00         78.08

        185.00         80.25

        190.00         82.42

        195.00         84.59

        200.00         86.76

----------------------------------------

And the plot will displays as shown in below Figure 1,

From the output of the MATLAB, the height of the water tower is approximately just below $190\text{ft}$ when the pressure $80\text{psi}$$\left(1\frac{\text{lb}}{{\text{in}}^{\text{2}}}=1\text{psi}\right)$ is created.

Conclusion:

Thus, the relationship between height of the water above ground in the water tower and water pressure in pipeline at the base of the tower is shown by creating a Table in MATLAB and the height of the water tower is approximately just below $190\text{ft}$ when the pressure $80\text{psi}$ is created.