add errata, fix typos

uni/mmme/2047_thermodynamics_and_fluid_dynamics/pumps.md

@@ -11,6 +11,16 @@ exercise_sheets: [ ./exercise_sheets/Turbomachinery-problems.pdf]
 
 Turbomachinery are rotating devices that add (pump for liquids; fan, blower, or compressor for gases at <0.02, <1 bar, and > 1 bar respectively) or extract (turbine) energy from a fluid.
 
+# Errata
+
+## Worked Example 3 Diameter Incorrect (lecture slides 42, lecture notes p. 13)
+
+Question specifies 21" diameter, but should be 32" diameter I think??
+Solution provided in lecture slides continues to use 21" dia, but measures
+from graph as if is 32".
+Weird.
+
+
 # Positive Displacement (PD) Pumps
 
 - PD pumps force fluid along using volume changes (e.g. bike pumps, the heart)
@@ -112,7 +122,7 @@ This is where cavitation occurs and causes wear on the blade.
 The following conditions must be satisfied to prevent cavitation:
 
 \begin{equation}
-H_i - \frac{p_v}{\rho g} > \text{NSPSH}
+H_i - \frac{p_v}{\rho g} > \text{NPSH}
 \end{equation}
 
 where $H_i = \frac{p_i}{\rho g} + \frac{v_i^2}{2g}$ is total head at inlet, $p_v$ is saturation
@@ -146,8 +156,8 @@ Pi-theorem allows the following coefficients to be derived:
 Therefore it can be expressed that:
 
 \begin{align*}
-C_H &= g_1(C_Q, \text{Re}, \frac{\epsilon}{D} \\
-C_P &= g_2(C_Q, \text{Re}, \frac{\epsilon}{D}
+C_H &= g_1\left(C_Q, \text{Re}, \frac{\epsilon}{D}\right) \\
+C_P &= g_2\left(C_Q, \text{Re}, \frac{\epsilon}{D}\right)
 \end{align*}
 
 However for pumps it is assumed that Reynolds number and roughness parameter are constant