Answer to Question #191133 in Mechanical Engineering for Srn

Question

A drinking container has a parabolic cross section according to the x equation (the yz plane is the symmetrical plane of the drinking place and the z-axis stretches in the direction of the drinker's axis) The drinking place is 1 meter long, with both vertical end walls, and the greatest depth is 40 cm. With the exact analytical method, calculate:

a. The volume of drinking water that can be accommodated by drinking containers (in liters

b. The amount of force due to water gage pressure on the end wall of the drinking place (in N)

c. Using the numerical method and the help of the Matlab function calculate the force magnitude use the integers that got fromq questionpoint b.

Answer 1

For a parabolic surface of r radius $r(x)=a\sqrt{x}$ at x=0 $\implies r(0)=a\sqrt{0}=0$

at x=h $\implies r(h)=a\sqrt{h}=r \implies a=\frac{r}{\sqrt{h}}$

Now $r(x)=\frac{r}{\sqrt{h}}\sqrt{x}$

$V=\pi \int_a^b(r(x))^2dx =\frac{\pi r^2}{h} \int_0^hxdx=\frac{\pi r^2h}{2}=\frac{\pi*502*20}{2}=50000 \pi cm^3$

Force = $9.8*1000 *50 \pi=1539380.4 N$