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fix typos in turbomachinery notes

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Akbar Rahman 2023-04-23 17:09:25 +01:00
parent 519d3e37f0
commit 6ec65bd5ec
Signed by: alvierahman90
GPG Key ID: 20609519444A1269
2 changed files with 10 additions and 10 deletions
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14
uni/mmme/2047_thermodynamics_and_fluid_dynamics/pumps.md
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@ -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*}

6
uni/mmme/2047_thermodynamics_and_fluid_dynamics/turbines.md
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@ -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: