Question

Write a C program to compute volume of liquid in elliptical storage tank. Dimension of the tank is given (unit in meters] width w, height h, and length len. The depth of the tank is measured by a depth gauge, which is already calibrated in units of 10 cm (e.g. 20 cm or 800 cm, only a multiplication of 10 cm). To compute the volume more precisely, use cross-sectional area of the tank for each given depth by trapezoidal method integration. Next, multiply this by the length of the tank. If the tank has width w and height h (in centimeters), the focal radii of the cross section are a = " and b= . Then the equation of the ellipse is: 1 62 y = f(x) Figure 2: Trapezoidal method for integration The function is divided into many sub-intervals (let's say n intervals) and each interval is approx- imated by a Trapezium. Then the area of trapeziums is calculated to find the integral which is basically the area under the curve. The more is the number of trapeziums used, the better is the approximation. Formula: (a) +2f(a + 8) +2f(a +28) + ... + f(b)) 12 Assuming a fixed size h for each set of parameters, obtain the value of h by considering the formula: delta = height/n (and not depth/n), and sub-intervals n=10000.

Maybe it’s easier to imagine the tank on its side so that the depth gauge is inserted horizontally if you do this you must express the equation as a function of y and integrate that function.

Please use the ellipse formula, and compute the volume of liquid by trapezoidal integral and function you altered for the ellipse formula. MUST contain following function:

Void trapezoidal_integral (double depth, int n, double width, double height, double length, double *integral_result)

Sample output:

Enter the width of the tank (in meters): 9

Enter the height of the tank (in meters): 10

Enter the length of the tank (in meters): 12

Enter the specific depth on the measuring stick (in centimeters): 900

Depth 900 cm

Volume 804.02 cubic meters

Please use C as programming language. thx

Answer 1

C CODE :

#include <stdio.h>

#include <math.h>

#include <stdlib.h>

double WIDTH;

double HEIGHT;

double LENGTH;

double DEPTH;

typedef double (*DFD) (double);

//Function of y in terms of x

double function (double x)

{

double a = HEIGHT / 2.0;

double b = WIDTH / 2.0;

double y = (b / a) * sqrt (a * a - x * x);

return y;

}

// Integration function - modified we are passing directly a and b from ellipse equation

double trapezoidal_integral (DFD f ,double a, double b, int n)

{

double x, delta, sum=0.0;

int i=0;

delta = (b-a)/ n;

// integration logic

sum = (function(a) + function(b))/2;

for (i=1, x = a + delta; i < n; i++, x += delta)

sum += function(x);

return sum * delta;

}

int main ()

{

printf ("Enter Width of the tank (in meters):\n");

scanf ("%lf",&WIDTH);

  

printf ("Enter Height of the tank (in meters):\n");

scanf ("%lf",&HEIGHT);

  

printf ("Enter Length of the tank(in meters):\n");

scanf ("%lf",&LENGTH);

  

printf ("Enter specific depth on measuring stick (in centimeters):\n");

scanf ("%lf",&DEPTH);

double h = DEPTH / 100.0;

  

double area = 2.0 * trapezoidal_integral (&function, HEIGHT / 2 - h, HEIGHT / 2, 100);

  

// volume is croos section area times lenth of tank

  

double volume = area * LENGTH;

printf ("Depth %f cm: Volume %.6lf cubic metres\n",DEPTH, volume);

return 0;

}

SCREENSHOT FOR CODE :

OUTPUT :