From 6ec65bd5ec9ee49009878fd5e1e3b50533a35907 Mon Sep 17 00:00:00 2001 From: Alvie Rahman Date: Sun, 23 Apr 2023 17:09:25 +0100 Subject: [PATCH] fix typos in turbomachinery notes --- .../pumps.md | 14 +++++++------- .../turbines.md | 6 +++--- 2 files changed, 10 insertions(+), 10 deletions(-) diff --git a/uni/mmme/2047_thermodynamics_and_fluid_dynamics/pumps.md b/uni/mmme/2047_thermodynamics_and_fluid_dynamics/pumps.md index c30d2a2..d412f2a 100755 --- a/uni/mmme/2047_thermodynamics_and_fluid_dynamics/pumps.md +++ b/uni/mmme/2047_thermodynamics_and_fluid_dynamics/pumps.md @@ -51,7 +51,7 @@ Turbomachinery are rotating devices that add (pump for liquids; fan, blower, or Derivation in slides (p. 23-25). \begin{align} -\frac{w_s}{g} - \left(\frac{u_2-_1-q}{g}\right) = \left(\frac{p_2}{\rho g} + z_2 + \frac{v_2^2}{2g}\right) -\left(\frac{p_1}{\rho g} + z_1 + \frac{v_1^2}{2g}\right) \\ +\frac{w_s}{g} - \left(\frac{u_2-_1-q}{g}\right) &= \left(\frac{p_2}{\rho g} + z_2 + \frac{v_2^2}{2g}\right) -\left(\frac{p_1}{\rho g} + z_1 + \frac{v_1^2}{2g}\right) \\ H_s - H_f &= H = H_{T,2} - H_{T,1} \nonumber \end{align} @@ -136,17 +136,17 @@ $$P = f_2(Q, D, n, \rho, \mu, \epsilon)$$ Pi-theorem allows the following coefficients to be derived: \begin{align} -\Pi_1 &= C_H = \frac{gH}{n^2D^2} &\text{Head coefficient} -\Pi_2 &= C_P = \frac{P}{\rho n^3D^5}&\text{Power coefficient} -\Pi_3 &= C_Q = \frac{Q}{nD^3}&\text{Capacity coefficient} -\Pi_4 &= \text{Re} = \frac{\rho nD^2}{\mu}&\text{Reynolds Number} +\Pi_1 &= C_H = \frac{gH}{n^2D^2} &\text{Head coefficient} \\ +\Pi_2 &= C_P = \frac{P}{\rho n^3D^5}&\text{Power coefficient} \\ +\Pi_3 &= C_Q = \frac{Q}{nD^3}&\text{Capacity coefficient} \\ +\Pi_4 &= \text{Re} = \frac{\rho nD^2}{\mu}&\text{Reynolds Number} \\ \Pi_5 &= = \frac{\epsilon}{D}&\text{Roughness Parameter} \end{align} Therefore it can be expressed that: \begin{align*} -C_H &= g_1(C_Q, \text{Re}, \frac{\epsilon}{D} +C_H &= g_1(C_Q, \text{Re}, \frac{\epsilon}{D} \\ C_P &= g_2(C_Q, \text{Re}, \frac{\epsilon}{D} \end{align*} @@ -159,7 +159,7 @@ Similar pumps are those which have the same design, other than the dimensions. Therefore it can be written that: \begin{align*} -C_H &\approx g_3(C_Q) +C_H &\approx g_3(C_Q) \\ C_P &\approx g_4(C_Q) \end{align*} diff --git a/uni/mmme/2047_thermodynamics_and_fluid_dynamics/turbines.md b/uni/mmme/2047_thermodynamics_and_fluid_dynamics/turbines.md index a23da9e..b14c76d 100755 --- a/uni/mmme/2047_thermodynamics_and_fluid_dynamics/turbines.md +++ b/uni/mmme/2047_thermodynamics_and_fluid_dynamics/turbines.md @@ -21,9 +21,9 @@ There are two types of turbines: The dimensionless groups are the same as in pumps: \begin{align} -C_H &= \frac{gH}{n^2D^2} &\text{Head coefficient} -C_P &= \frac{P}{\rho n^3D^5}&\text{Power coefficient} -C_Q &= \frac{Q}{nD^3}&\text{Capacity coefficient} +C_H &= \frac{gH}{n^2D^2} &\text{Head coefficient} \\ +C_P &= \frac{P}{\rho n^3D^5}&\text{Power coefficient} \\ +C_Q &= \frac{Q}{nD^3}&\text{Capacity coefficient} \\ \end{align} However, in a turbine the efficiency is written as: