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====== Differences ====== This shows you the differences between two versions of the page.

--- gibson:teaching:spring-2016:math445:lab9 [2016/03/29 06:22]
gibson [Math 445 lab 9: 3d graphics]
+++ gibson:teaching:spring-2016:math445:lab9 [2016/03/31 09:39] (current)
vining
@@ Line 74: / Line 74: @@
 </code>
-===== Problem 5: quiver plot =====
+===== Problem 6: quiver plot =====
 The function
@@ Line 87: / Line 87: @@
 **(b)** In a gentle rainstorm, water will flow down the mountains in the direction of steepest descent, i.e. along the negative of the gradient of $f$. Find the gradient of $f$ using elementary calculus, then make an $x,y$ plot with both contours of the mountain height $f$ and a quiver plot showing the direction of flow of rainwater.
+===== Problem 7: inviscid fluid flow within a square corner =====
+The inviscid 2d fluid flow within a square corner with solid walls at $x=0$ and $y=0$ and the domain $x \geq 0$ and $y \geq 0$ has velocity components
+\begin{eqnarray*}
+v_x &= v_0 \, x \\
+v_y &= -v_0 \, y
+\end{eqnarray*}
+Make a quiver plot of this flow for $0 \leq x \leq 1$ and $0 \leq y \leq 1$, and with $v_0 = 1$. Label the axes and title the plot.
+===== Problem 8: inviscid fluid flow past a semicircular bump =====
+The inviscid 2d fluid flow past a semicircular bump of radius $a$ centered at the origin on a flat wall at $y=0$ has velocity components
+\begin{eqnarray*}
+v_x &= v_0 \left(1 - a^2 \frac{x^2 - y^2}{(x^2+y^2)^2}\right) \\
+v_y &= -2 a v_0 \frac{xy}{(x^2+y^2)^2}
+\end{eqnarray*}
+Make a quiver plot of this flow for $a=1$, $v_0=1$, $-3 \leq x \leq 3$ and $0 \leq y \leq 3$, excluding the interior of the bump, where $x^2 + y^2 < a^2$. Draw a blue curve that shows the surface of the semicircular bump. Make the $x$ and $y$ axis have the same scale, label the axes, and title the plot.
 ===== Bonus =====

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