formulari tecnologia industrial

Principis de màquines
$$\sum \vec F_x = 0 \; \sum \vec F_y = 0 \; \sum \vec M_z = 0$$

$$M_{O} = F · d \quad \Gamma= F· D$$

$$W = F · s · \cos \alpha \quad E_m = E_c +E_p$$

$$E_c = \frac{1}{2}mv^2 \quad E_p = mgh \quad P = \frac{W}{\Delta T}$$

$$F = kx \quad W_{1-2}= \frac{1}{2}k(x_1^2-x_2^2)$$

$$W =M · \Delta \phi \quad E_c = \frac{1}{2} \omega^2 I \quad P=\Gamma·\omega$$

$$\phi = \phi_0 + \omega_0t + \frac{1}{2}\alpha t^2 \quad \alpha=\frac{\Delta \omega}{\Delta t} \quad \eta= \frac{W_u}{W_c}$$

$$p= \frac{F}{A} \quad 1\ atm = 101300 \ Pa \quad T_F =\frac{9}{5}T_c+32$$

$$P_c = P_c(CN)·\frac{p}{101300} ·\frac{273}{273+T} \quad Q= m·c_e \Delta T \quad Q= mL$$

$$\frac{p_1·V_1}{T_1}= \frac{p_2·V_2}{T_2} \quad p·V = n·R·T \quad W_{1-2} = p· \Delta V$$

$$W_{1-2} = n·R·T \ln{\frac{V_2}{V_1}} \quad W_{1-2} = \frac{p_2·V_2-p_1·V_1}{1-\gamma}$$

$$pV^\gamma = K \quad T·V^{\gamma-1} = K$$

Màquines tèrmiques
$$\eta_c = 1-Q_c \quad \eta_s=\frac{\eta_t}{\eta_c}$$

$$\Delta S_i = \frac{\left | Q \right |}{T_i} \quad W_p = T_c· \Delta S_t$$

$$V_c = \pi · r^2 c \quad r = \frac{V_{màx}}{V_{mín}}$$

$$COP = \frac{Q_c}{W} \quad COP_c= \frac{T_c}{T_h-T_c}$$

$$W = \frac{\left | Q_h \right |}{1+COP}$$

Oleohidràulica
$$q = \frac{V}{t} = A · v$$

$$P = \frac{p·V}{t} = p · q$$

$$p = \frac{F}{A}$$

Electromagnetisme i corrent altern
$$X_L = L \omega = L ·2 · \pi$$

$$X_c = \frac {1}{C\omega}= \frac {1}{C · 2 · \pi · f}$$

$$P = VI = RI^2$$

$$p = 3R_L · I^2 = \frac{3 \rho · L ·I^2}{s}$$

$$I = \frac{P}{\sqrt{3}·V·\cos{\varphi}}$$

I així demostrem que $P = \frac{\rho·V^3}{t} = p · q$