Challenge Team Interim Report

 Team Number: 031 School Name: Cuba High School Area of Science: Environmental Project Title: The Effect of Hydrofoils on Stream Beds
 Abstract Interim Final Report

Problem Definition

Erosion along riverbeds and arroyos is a problem in many places. It affects roads, houses, and both public and private property. Current thought is that due to the dynamics of the shape of a hydrofoil, which in this instance is the same shape as the cross-section of an airplane wing, which produces lift, the stationary hydrofoil can divert water. The focus of this project is to write a C++ program that will determine if the dynamics of a hydrofoil can divert water to decrease erosion along the banks of an arroyo or riverbed. This program will also attempt to determine how much water a hydrofoil will divert.

Computational Plan

This program uses a formula that gives the difference in pressure between a point on the top of a hydrofoil and a point on the bottom. This is what coding we have finished up to this point.

`#include   `

float v; //initial velocity
float vt; //top velocity
float vb; //bottom velocity
float pt; //top pressure differential
float pb; //bottom pressure differential
float k; //theta
float w=62.4; //weight of water in lbs/ft^3
float g=32.2; //force of gravity in ft/sec^2 finalpressure();
retreive();
p-top();
p-bot();
main()
{
retreive();
p-top();
p-bot();
finalpressure();
}
retreive() //gets input from user
{
cout<<"This program assumes that the velocity on a certain point on top of the aerofoil has a velocity of 3 ft/sec more than the initial velocity and the velocity on a certain point on the bottom of the aerofoil has the velocity of 2 ft/sec less than the initial velocity \n";
cout<<"Enter the Beginning Velocity \n";
cin>>v;
vt=v+3;
vb=v-2;
return vb, vt, v;
}
p-top() //function that figures the pressure difference between the initial point and a certain point on top
{
k=w/g;
pt=(k*(v*v)/2)*(1-((vt/v)*(vt/v)));
return pt;
}
p-bot() //function that figures pressure difference between the initial point and a certain point on the bottom
{
k=w/g;
pb=(k*(v*v)/2)*(1-((vb/v)*(vb/v)));
return pb;
}
finalpressure()
{
float pd; //final pressure differencial
if (pt<=0)
{
pd=pt+pb;
}
else
{
pd=pt-pb;
}
cout<<"The pressure difference between the bottom point and top point is "< }

Progress to Date

We have had many ups and downs in trying to work on our project, but we still remain hopeful that we can accomplish something great. Due to the fact that our project deals with somewhat unknown subject matter it has been hard to gather information. But, we still have made some progress with what we have found. We have contacted different people who have worked with projects similar to ours in hopes they may be able to lend us some general information or help in any way. Also, we have contacted different scientists and engineers that deal with the dynamics and engineering of hydrofoil types. The father of one of our team members is an engineer and he has helped us in understanding the different equations that determine pressures and such of hydrofoils. We have found a few equations, which we can program to calculate the pressure differences and lift. The equation that finds lift for the whole hydrofoil is fairly advanced calculus and we are in the process of talking to engineers and others to help us understand how this equation works.

Research

Erosion is a serious problem in the environment. It can also cause problems for humans. Erosion is the physical movement of soil particles (Union of International Associations). One cause of erosion is the movement of water in the meander of a river. Most rivers and streams naturally meander. In fact, 85% of the world's rivers meander. This occurs naturally in nature. One example of meandering is when a drop of water is placed on a tilted plane. It does not flow straight, rather it meanders (Rutten). One possible solution to erosion in meandering rivers or arroyos is placing hydrofoils into the river or arroyo, to slow down the speed of the water, thus decreasing the depletion of the soil at the meander. Foil is another name for wings. A hydrofoil is the name of a wing that "flies" in water. Most hydrofoils are used for boats for the purpose of lifting the hull of the boat out of the water. Hydrofoils are smaller than airplane wings because water is one thousand times more dense than air. This greater density enables the hydrofoil to make enough lift to keep the boat above the water (Drela, Finberg, and Wall). Wings change the speed of air (which is described as a fluid) or water. The air above a wing travels fast, and below the wing, the air travels slower. Bernoulli's principal states that air with high velocity has low pressure and air with a low velocity has high pressure. When lift is produced the air that travels above the wing travels in less time. Thus, placing hydrofoils in a strategic place can slow the water at the meander of a stream down (Denker).

Results Expected

Our C++ program is expected to output the pressure differential and tell us how much water a hydrofoil will divert. Due to the dynamics of aerofoils and hydrofoils, the velocity slows on one side. This will cause sediment to fall out of the water and not rub against the soil at high speeds and will therefore prevent erosion at meanders of a river or of an arroyo. This program will tell us whether this method of approach will divert the water away from the banks at least somewhat.

Bibliography

Denker, John S. Airfoils and Airflow [Chapter 3 of See How it Flies] 1996. http://www.monmouth.com/~jsd/fly/how/htm/airfoils.html. Drela Mark, Finberg Steve, Wall Matthew. Hydrofoil Basics. 1995 http://lancet.mit.edu/decavitator/Basics.html. Rutten Luke. "Gel-135G Rivers of California Lab 4: Channel Planform Patterns. April 30, 1997. http://www.-geology.ucdavis.edu/~GEL135G/labfour.htm. Union of International Associations. Soil Erosion. November 24, 1998, http://www.uia.org/uiademo/pro/d0949.htm. Crowe, Clayton and Robertson, John , Engineering Fluid Mechanics, Boston: Houghton Mifflin Company, 1975.

Team Members