fix bernoulli more

content/formulas/bernoullis-principle/index.md

@@ -4,12 +4,12 @@ description: "The relation between various sources of pressure in a fluid."
 summary: "The relation between various sources of pressure in a fluid."
 tags: ["physics", "fluid mechanics"]
 date: 2024-02-07
-latex:  P + \frac{1}{2} \rho v^2 + \rho g h = const
+latex:  P + \frac{1}{2} \rho v^2 + \rho g h = \text{const}
 ---
 
 {{< katex >}}
 
-The formula for Bernoulli's Principle (also known as Bernoulli's Equation) states that for two points along the streamline of an incompressible, inviscid, steady-flow fluid, the sum of the pressure, kinetic energy per unit volume, and potential energy per unit volume remains constant:
+The formula for Bernoulli's Principle (also known as Bernoulli's Equation) states that for two points along the streamline of an incompressible, inviscid, steady-flow fluid, the sum of the pressure, kinetic energy per unit volume, and potential energy per unit volume remains constant. It has the following forms:
 
 ## Pressure Form
 
@@ -25,15 +25,19 @@ Where
 
 It can be also be written by stating that the sum of the quantities remain constant:
 
-$$ P + \frac{1}{2} \rho v^2 + \rho g h = const $$
+$$ P + \frac{1}{2} \rho v^2 + \rho g h = \text{const} $$
 
 
 ## Energy Form
 
+$$ \frac{P}{\rho} + \frac{1}{2} v^2 + g h = \text{const} $$
+
 $$ \frac{P_1}{\rho} + \frac{1}{2} v_1^2 + g h_1 = \frac{P_2}{\rho} + \frac{1}{2} v_2^2 + g h_2 $$
 
 ## Head Form
 
+$$ \frac{P}{\gamma} + \frac{v^2}{2g} + h = \text{const} $$
+
 $$ \frac{P_1}{\gamma} + \frac{v_1^2}{2g} + h_1 = \frac{P_2}{\gamma} + \frac{v_2^2}{2g} + h_2 $$
 
 Where