Gebruiker:DeSinT/Zandbak/Vloeistofmechanica

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1 1.1
- 1.1 2
- 1.2 3
- 1.3 7
- 1.4 9
- 1.5 14
- 1.6 38
- 1.7 39
- 1.8 40
- 1.9 47

[bewerk] 1.1

[bewerk] 2

$v=0 \mbox{, in}\left [m/s \right]$

$v \neq 0 \mbox{, in} \left [m/s \right]$

$\frac{\partial V} {\partial t} = 0$

$\frac{\partial V} {\partial t} \neq 0$

$\frac{\partial V} {\partial x} = 0$

$\frac{\partial V} {\partial x} \neq 0$

[bewerk] 3

$p=\rho\cdot g\cdot h \Rightarrow h=\frac{p}{\rho \cdot g}$

$q_v=\bar{v}\cdot A \mbox{, in} \left [m^3/s \right ]$

[bewerk] 7

$F_{hydrostatisch}=p_{gemiddeld}\cdot A = \frac{1}{2}\cdot \rho \cdot g\cdot\ h *h\cdot b = \frac{1}{2}\cdot \rho\cdot h^2\cdot b$

$\begin{array}{rcl} F \cdot a & = & \sum p \cdot b \cdot dy \cdot y \\ F \cdot a & = & \int p \cdot b \cdot y \cdot dy \\ F \cdot a & = & \int \rho \cdot g \left ( h - y \right ) \cdot b \cdot y \cdot dy \\ \frac{1}{2} \cdot {\color{Red}\rho} \cdot {\color{Red}g} \cdot h^2 \cdot {\color{Red}b} \cdot a & = & \int {\color{Red}\rho} \cdot {\color{Red}g} \cdot \left ( h - y \right ) \cdot {\color{Red}b} \cdot y \cdot dy \\ \frac{1}{2} \cdot h^2 \cdot a & = & \int \left ( h - y \right ) \cdot y \cdot dy \\ \frac{1}{2}h^2 \cdot a & = & \int \left ( h \cdot y - y^2 \right ) \cdot dy \\ \frac{1}{2}h^2 \cdot a & = & \int_{y=0}^{y=h} \left ( h \cdot y - y^2 \right )\, \cdot dy \\ \frac{1}{2}h^2 \cdot a & = & \left [h \cdot \frac{1}{2}y^2-\frac{1}{3}y^3 \right ]_{y=o}^{y=h} \\ \frac{1}{2}h^2 \cdot a & = & \left [h \cdot \frac{1}{2}h^2-\frac{1}{3}h^3 \right ] - \left [0-0 \right ] = \frac{1}{2}h^3-\frac{1}{3}h^3 \\ \frac{1}{2}h^2 \cdot a & = &\frac{1}{6}h^3 \\ \frac{1}{2} \cdot a & = & \frac{1}{6}h \\ a & = & \frac{1}{3}h \end{array}$

[bewerk] 14

$\begin{matrix} z_1+h_1=z_2+h_2=z_3+H_3=\mbox{constant} \end{matrix}$

[bewerk] 38

$H=z+\frac{p}{\rho \cdot g} + \frac {v^2}{2g} = \mbox{constant, in} \left [m \right]$

[bewerk] 39

$q_v=\mbox{constant} \Rightarrow v_1 \cdot A_1 = v_2 \cdot A_2 = v_3 \cdot A_3$

$H=z_1+\frac{p_1}{\rho \cdot g} + \frac {v_1^2}{2g} = z_2+\frac{p_2}{\rho \cdot g} + \frac {v_2^2}{2g} = z_3+\frac{p_3}{\rho \cdot g} + \frac {v_3^2}{2g}$

$\mbox{pi}\mathrm{\ddot{e}}\mbox{tzometrisch niveau (p.n.)} = z + \frac{p}{\rho \cdot g}$

[bewerk] 40

$H=z_1+\frac{p_1}{\rho \cdot g} + \frac {v_1^2}{2g} = z_2+\frac{p_2}{\rho \cdot g} + \frac {v_2^2}{2g} + \Delta H_{1-2}$

[bewerk] 47

$\begin{array}{rclcl} E_{totaal} & = & E_{potentieel} + E_{kinetisch} \mbox{, in} \left [Nm \right] \\ E_{totaal} & = & m \cdot g \cdot \left (z+h \right ) + \frac{1}{2}\cdot m \cdot v^2 \\ \frac{E_{totaal}}{m \cdot g} & = & z + h + \frac{v^2}{2g} & = & H \\ \frac{E_{totaal}}{m \cdot g} & = & H \\ \frac{E_{totaal}}{m \cdot g} & \Rightarrow & E_{totaal} = m \cdot g \cdot H ;\ \ m=\rho \cdot V & \Rightarrow & E_{totaal} = \rho \cdot V \cdot g \cdot H \\ \end{array}$

$\begin{array}{ccc} \Delta E & = & \rho \cdot \Delta V \cdot g \cdot H \\ dE & = & \rho \cdot dV \cdot g \cdot H \end{array}$

$P \equiv \frac{dE}{dt} = \rho \cdot \frac{dV}{dt} \cdot g \cdot H; \ \ q_v=\frac{dV}{dt} \Rightarrow P= \rho \cdot g \cdot q_v \cdot H \mbox{, in} \left [Nm/s \right ]; \left [J/s \right ]; \left [W \right ]$