NUMERICAL PROJECT

ME $325$ THERMAL FLUID SCIENCES I

Fall $2024$

Due Date: December $11$th by $2$ pm $.$

Submit report and Matlab program to Canvas.

Late reports will not be accepted.

Note: Must program in Matlab.

Problem

You are a test engineer and are working on the test cart shown below. A tank rolls along the guide wire with pulleys as shown. A scoop is attached to the bottom of the tank and is partially immersed a distance $h$ into the water. It scoops water from the reservoir surface into the tank as a means of stopping the tank. Your supervisor needs to know the scoop's immersion length to decelerate the tank within a maximum distance of $L=10m.$ You are asked to determine the distance traveled by the tank based on the scoop immersion length $h.$ You decide to model the tank and perform a parametric study to determine the tank distance as a function of immersion length.

The cart has an initial velocity of $V=12\frac{m}{s}$ and is initially empty. The scoop width is $w=80$ cm $.$ The wall of the tank is made of steel and has a mass of $m_t=14\mathrm{.}5kg.$ You decide to include the drag force of air flowing around the tank. The equation for the drag force is

$F_D=C_D{V}^2$

where $C_D=2\mathrm{.}01N-\frac{s^2}{m^2}$ is the drag force coefficient and $V$ is the tank velocity $\frac{m}{s}.$ The pulley friction equation is

$F_{\text{f}\text{r}\text{i}\text{c}\text{i}\text{t}\text{i}\text{o}\text{n}}=C_f{F}_W$

where $C_f=0\mathrm{.}005$ is the friction coefficient and $F_w$ is the tank weight $[$N$].$ You decide to neglect the momentum of the fluid inside the tank. The density of the water is $=998k\frac{g}{m^3}.$ Acceleration of gravity is $g=9\mathrm{.}81\frac{m}{s^2}.$

You are interested in how the system variables affect the tank$\text{'}$s distance traveled. Perform a parametric study of the scoop immersion length from $1$ cm to $18$ cm and plot distance traveled versus immersion length. For this range, also plot the effect of immersion length on $($i$)$ time to decelerate to zero velocity, and $($ii$)$ amount of water collected. Explain why the plots are shaped the way they are. Also present the magnitude of forces during deceleration from $0\mathrm{.}5$ s to the final time of zero velocity for the case where it travels $L=10m$ and discuss the individual force contributions in stopping the tank.

You are to present your results back to your supervisor in a report. Please follow the report format provided by the supervisor.