Wysokość rozporządzalna

$$H_{r} = \frac{p_{b}}{\text{ϱg}} + \frac{v^{2}}{2g} + z = 100,00dm + 0 + 10,51dm = 110,51dm$$

$$v = \frac{q_{v}}{A} = \frac{4q_{v}}{\pi d_{1}^{2}}$$

Straty miejscowe

$${h}_{s_{1}}^{m} = \xi\frac{v^{2}}{2g} = \xi\frac{\left( \frac{q_{v}}{A} \right)^{2}}{2g} = \xi\frac{\left( \frac{4q_{v}}{\pi d_{1}^{2}} \right)^{2}}{2g} = 0,5\frac{\left( \frac{4 \bullet 190\frac{dm^{3}}{h}}{\pi \bullet \left( 0,123dm \right)^{2}} \right)^{2}}{2 \bullet 1271376000\frac{\text{dm}}{h^{2}}} = 0,5\frac{255686026,1\frac{dm^{2}}{h^{2}}}{2542752000\frac{\text{dm}}{h^{2}}} = 0,0503dm$$

$${h}_{s_{4}}^{m} = \xi\frac{v^{2}}{2g} = \xi\frac{\left( \frac{q_{v}}{A} \right)^{2}}{2g} = \xi\frac{\left( \frac{4q_{v}}{\pi d_{1}^{2}} \right)^{2}}{2g} = 1 \bullet \frac{\left( \frac{4 \bullet 190\frac{dm^{3}}{h}}{\pi \bullet \left( 0,123dm \right)^{2}} \right)^{2}}{2 \bullet 1271376000\frac{dm^{2}}{h}} = \frac{255686026,1\frac{dm^{2}}{h^{2}}}{2542752000\frac{dm^{2}}{h}} = 0,1006dm$$

$${h}_{s_{5}}^{m} = \xi\frac{v^{2}}{2g} = \xi\frac{\left( \frac{q_{v}}{A} \right)^{2}}{2g} = \xi\frac{\left( \frac{4q_{v}}{\pi d_{1}^{2}} \right)^{2}}{2g} = 0,5\frac{\left( \frac{4 \bullet 190\frac{dm^{3}}{h}}{\pi \bullet \left( 0,123dm \right)^{2}} \right)^{2}}{2 \bullet 1271376000\frac{dm^{2}}{h}} = 0,5\frac{255686026,1\frac{dm^{2}}{h^{2}}}{2542752000\frac{dm^{2}}{h}} = 0,0503dm$$

$${h}_{s_{6}}^{m} = \xi\frac{v^{2}}{2g} = \left\lbrack 1 - \left( \frac{d_{2}}{d_{1}} \right)^{2} \right\rbrack \bullet \frac{\left( \frac{q_{v}}{A} \right)^{2}}{2g} = \left\lbrack 1 - \left( \frac{d_{2}}{d_{1}} \right)^{2} \right\rbrack \bullet \frac{\left( \frac{4q_{v}}{\pi d_{2}^{2}} \right)^{2}}{2g} = \left\lbrack 1 - \left( \frac{0,083dm}{0,123dm} \right)^{2} \right\rbrack \bullet \frac{\left( \frac{4 \bullet 190\frac{dm^{3}}{h}}{\pi \bullet \left( 0,083dm \right)^{2}} \right)^{2}}{2 \bullet 1271376000\frac{dm^{2}}{h}} = 0,545 \bullet \frac{1233147622\frac{dm^{2}}{h^{2}}}{2542752000\frac{dm^{2}}{h}} = 0,264dm$$

$${h}_{s_{7}}^{m} = \xi\frac{v^{2}}{2g} = \left\lbrack 1 - \left( \frac{d_{3}}{d_{2}} \right)^{2} \right\rbrack \bullet \frac{\left( \frac{q_{v}}{A} \right)^{2}}{2g} = \left\lbrack 1 - \left( \frac{d_{3}}{d_{2}} \right)^{2} \right\rbrack \bullet \frac{\left( \frac{4q_{v}}{\pi d_{3}^{2}} \right)^{2}}{2g} = \left\lbrack 1 - \left( \frac{0,0715dm}{0,083dm} \right)^{2} \right\rbrack \bullet \frac{\left( \frac{4 \bullet 190\frac{dm^{3}}{h}}{\pi \bullet \left( 0,0715dm \right)^{2}} \right)^{2}}{2 \bullet 1271376000\frac{dm^{2}}{h}} = 0,258 \bullet \frac{2239253553\frac{dm^{2}}{h^{2}}}{2542752000\frac{dm^{2}}{h}} = 0,227dm$$

$${h}_{s_{8}}^{m} = \xi\frac{v^{2}}{2g} = \left( \frac{d_{1}}{d_{3}} - 1 \right)^{2} \bullet \frac{\left( \frac{q_{v}}{A} \right)^{2}}{2g} = \left( \frac{d_{1}}{d_{3}} - 1 \right)^{2} \bullet \frac{\left( \frac{4q_{v}}{\pi d_{1}^{2}} \right)^{2}}{2g} = \left( \frac{0,123dm}{0,0715dm} - 1 \right)^{2} \bullet \frac{\left( \frac{4 \bullet 190\frac{dm^{3}}{h}}{\pi \bullet \left( 0,123dm \right)^{2}} \right)^{2}}{2 \bullet 1271376000\frac{dm^{2}}{h}} = 0,519 \bullet \frac{2239253553\frac{dm^{2}}{h^{2}}}{2542752000\frac{dm^{2}}{h}} = 0,457\text{dm}$$

$${h}_{s_{9}}^{m} = \xi\frac{v^{2}}{2g} = \xi\frac{\left( \frac{q_{v}}{A} \right)^{2}}{2g} = \xi\frac{\left( \frac{4q_{v}}{\pi d_{1}^{2}} \right)^{2}}{2g} = 1 \bullet \frac{\left( \frac{4 \bullet 190\frac{dm^{3}}{h}}{\pi \bullet \left( 0,123dm \right)^{2}} \right)^{2}}{2 \bullet 1271376000\frac{dm^{2}}{h}} = \frac{255686026,1\frac{dm^{2}}{h^{2}}}{2542752000\frac{dm^{2}}{h}} = 0,1005dm$$

Straty liniowe

$$h_{s_{1}}^{l} = \lambda\frac{l_{1}}{d_{1}}\frac{v^{2}}{2g} = \frac{0,314}{\sqrt[4]{\text{Re}}}\frac{l_{1}}{d_{1}}\frac{\left( \frac{4q_{v}}{\pi d_{1}^{2}} \right)^{2}}{2g} = \frac{0,314}{\sqrt[4]{\frac{vd_{1}}{\upsilon}}}\frac{l_{1}}{d_{1}}\frac{\left( \frac{4q_{v}}{\pi d_{1}^{2}} \right)^{2}}{2g} = \frac{0,314}{\sqrt[4]{\frac{4q_{v}}{\pi d_{1}\upsilon}}}\frac{l_{1}}{d_{1}}\frac{\left( \frac{4q_{v}}{\pi d_{1}^{2}} \right)^{2}}{2g} = \frac{0,314}{\sqrt[4]{\frac{4 \bullet 190\frac{dm^{3}}{h}}{\pi \bullet 0,123dm \bullet 0,42192\frac{\text{dm}^{2}}{h}\ }}} \bullet 50 \bullet \frac{\left( \frac{4 \bullet 190\frac{dm^{3}}{h}}{\pi \bullet \left( 0,123dm \right)^{2}} \right)^{2}}{2 \bullet 1271376000\frac{dm^{2}}{h}} = \frac{0,314}{8,263} \bullet 50 \bullet \frac{255686026,1\frac{dm^{2}}{h^{2}}}{2542752000\frac{dm^{2}}{h}} = 0,191dm$$

$$h_{s_{2}}^{l} = \lambda\frac{l_{2}}{d_{1}}\frac{v^{2}}{2g} = \frac{0,314}{\sqrt[4]{\text{Re}}}\frac{l_{2}}{d_{1}}\frac{\left( \frac{4q_{v}}{\pi d_{1}^{2}} \right)^{2}}{2g} = \frac{0,314}{\sqrt[4]{\frac{vd_{1}}{\upsilon}}}\frac{l_{2}}{d_{1}}\frac{\left( \frac{4q_{v}}{\pi d_{1}^{2}} \right)^{2}}{2g} = \frac{0,314}{\sqrt[4]{\frac{4q_{v}}{\pi d_{1}\upsilon}}}\frac{l_{2}}{d_{1}}\frac{\left( \frac{4q_{v}}{\pi d_{1}^{2}} \right)^{2}}{2g} = \frac{0,314}{\sqrt[4]{\frac{4 \bullet 190\frac{dm^{3}}{h}}{\pi \bullet 0,123dm \bullet 0,42192\frac{\text{dm}^{2}}{h}\ }}} \bullet 100 \bullet \frac{\left( \frac{4 \bullet 190\frac{dm^{3}}{h}}{\pi \bullet \left( 0,123dm \right)^{2}} \right)^{2}}{2 \bullet 1271376000\frac{dm^{2}}{h}} = \frac{0,314}{8,263} \bullet 100 \bullet \frac{255686026,1\frac{dm^{2}}{h^{2}}}{2542752000\frac{dm^{2}}{h}} = 0,382dm$$

$$h_{s_{3}}^{l} = \lambda\frac{l_{3}}{d_{1}}\frac{v^{2}}{2g} = \frac{0,314}{\sqrt[4]{\text{Re}}}\frac{l_{2}}{d_{1}}\frac{\left( \frac{4q_{v}}{\pi d_{1}^{2}} \right)^{2}}{2g} = \frac{0,314}{\sqrt[4]{\frac{vd_{1}}{\upsilon}}}\frac{l_{3}}{d_{1}}\frac{\left( \frac{4q_{v}}{\pi d_{1}^{2}} \right)^{2}}{2g} = \frac{0,314}{\sqrt[4]{\frac{4q_{v}}{\pi d_{1}\upsilon}}}\frac{l_{3}}{d_{1}}\frac{\left( \frac{4q_{v}}{\pi d_{1}^{2}} \right)^{2}}{2g} = \frac{0,314}{\sqrt[4]{\frac{4 \bullet 190\frac{dm^{3}}{h}}{\pi \bullet 0,123dm \bullet 0,42192\frac{\text{dm}^{2}}{h}\ }}} \bullet 15 \bullet \frac{\left( \frac{4 \bullet 190\frac{dm^{3}}{h}}{\pi \bullet \left( 0,123dm \right)^{2}} \right)^{2}}{2 \bullet 1271376000\frac{dm^{2}}{h}} = \frac{0,314}{8,263} \bullet 15 \bullet \frac{255686026,1\frac{dm^{2}}{h^{2}}}{2542752000\frac{dm^{2}}{h}} = 0,0573dm$$

$$h_{s_{4}}^{l} = \lambda\frac{l_{4}}{d_{1}}\frac{v^{2}}{2g} = \frac{0,314}{\sqrt[4]{\text{Re}}}\frac{l_{4}}{d_{1}}\frac{\left( \frac{4q_{v}}{\pi d_{1}^{2}} \right)^{2}}{2g} = \frac{0,314}{\sqrt[4]{\frac{vd_{1}}{\upsilon}}}\frac{l_{4}}{d_{1}}\frac{\left( \frac{4q_{v}}{\pi d_{1}^{2}} \right)^{2}}{2g} = \frac{0,314}{\sqrt[4]{\frac{4q_{v}}{\pi d_{1}\upsilon}}}\frac{l_{4}}{d_{1}}\frac{\left( \frac{4q_{v}}{\pi d_{1}^{2}} \right)^{2}}{2g} = \frac{0,314}{\sqrt[4]{\frac{4 \bullet 190\frac{dm^{3}}{h}}{\pi \bullet 0,123dm \bullet 0,42192\frac{\text{dm}^{2}}{h}\ }}} \bullet 50 \bullet \frac{\left( \frac{4 \bullet 190\frac{dm^{3}}{h}}{\pi \bullet \left( 0,123dm \right)^{2}} \right)^{2}}{2 \bullet 1271376000\frac{dm^{2}}{h}} = \frac{0,314}{8,263} \bullet 50 \bullet \frac{255686026,1\frac{dm^{2}}{h^{2}}}{2542752000\frac{dm^{2}}{h}} = 0,191dm$$

$$h_{s_{5}}^{l} = \lambda\frac{l_{5}}{d_{2}}\frac{v^{2}}{2g} = \frac{0,314}{\sqrt[4]{\text{Re}}}\frac{l_{5}}{d_{2}}\frac{\left( \frac{4q_{v}}{\pi d_{2}^{2}} \right)^{2}}{2g} = \frac{0,314}{\sqrt[4]{\frac{vd_{2}}{\upsilon}}}\frac{l_{5}}{d_{2}}\frac{\left( \frac{4q_{v}}{\pi d_{2}^{2}} \right)^{2}}{2g} = \frac{0,314}{\sqrt[4]{\frac{4q_{v}}{\pi d_{2}\upsilon}}}\frac{l_{5}}{d_{2}}\frac{\left( \frac{4q_{v}}{\pi d_{2}^{2}} \right)^{2}}{2g} = \frac{0,314}{\sqrt[4]{\frac{4 \bullet 190\frac{dm^{3}}{h}}{\pi \bullet 0,083dm \bullet 0,42192\frac{\text{dm}^{2}}{h}\ }}} \bullet 30 \bullet \frac{\left( \frac{4 \bullet 190\frac{dm^{3}}{h}}{\pi \bullet \left( 0,083dm \right)^{2}} \right)^{2}}{2 \bullet 1271376000\frac{dm^{2}}{h}} = \frac{0,314}{9,117} \bullet 30 \bullet \frac{1233147622\frac{dm^{2}}{h^{2}}}{2542752000\frac{dm^{2}}{h}} = 0,835dm$$

$$h_{s_{6}}^{l} = \lambda\frac{l_{6}}{d_{3}}\frac{v^{2}}{2g} = \frac{0,314}{\sqrt[4]{\text{Re}}}\frac{l_{6}}{d_{3}}\frac{\left( \frac{4q_{v}}{\pi d_{3}^{2}} \right)^{2}}{2g} = \frac{0,314}{\sqrt[4]{\frac{vd_{3}}{\upsilon}}}\frac{l_{6}}{d_{3}}\frac{\left( \frac{4q_{v}}{\pi d_{3}^{2}} \right)^{2}}{2g} = \frac{0,314}{\sqrt[4]{\frac{4q_{v}}{\pi d_{3}\upsilon}}}\frac{l_{6}}{d_{3}}\frac{\left( \frac{4q_{v}}{\pi d_{3}^{2}} \right)^{2}}{2g} = \frac{0,314}{\sqrt[4]{\frac{4 \bullet 190\frac{dm^{3}}{h}}{\pi \bullet 0,0715dm \bullet 0,42192\frac{\text{dm}^{2}}{h}\ }}} \bullet 30 \bullet \frac{\left( \frac{4 \bullet 190\frac{dm^{3}}{h}}{\pi \bullet \left( 0,0715dm \right)^{2}} \right)^{2}}{2 \bullet 1271376000\frac{dm^{2}}{h}} = \frac{0,314}{9,463} \bullet 30 \bullet \frac{2239253553\frac{dm^{2}}{h^{2}}}{2542752000\frac{dm^{2}}{h}} = 0,877dm$$

$$h_{s_{7}}^{l} = \lambda\frac{l_{7}}{d_{1}}\frac{v^{2}}{2g} = \frac{0,314}{\sqrt[4]{\text{Re}}}\frac{l_{7}}{d_{1}}\frac{\left( \frac{4q_{v}}{\pi d_{1}^{2}} \right)^{2}}{2g} = \frac{0,314}{\sqrt[4]{\frac{vd_{1}}{\upsilon}}}\frac{l_{7}}{d_{1}}\frac{\left( \frac{4q_{v}}{\pi d_{1}^{2}} \right)^{2}}{2g} = \frac{0,314}{\sqrt[4]{\frac{4q_{v}}{\pi d_{1}\upsilon}}}\frac{l_{7}}{d_{1}}\frac{\left( \frac{4q_{v}}{\pi d_{1}^{2}} \right)^{2}}{2g} = \frac{0,314}{\sqrt[4]{\frac{4 \bullet 190\frac{dm^{3}}{h}}{\pi \bullet 0,123dm \bullet 0,42192\frac{\text{dm}^{2}}{h}\ }}} \bullet 48,5 \bullet \frac{\left( \frac{4 \bullet 190\frac{dm^{3}}{h}}{\pi \bullet \left( 0,123dm \right)^{2}} \right)^{2}}{2 \bullet 1271376000\frac{dm^{2}}{h}} = \frac{0,314}{8,263} \bullet 48,5 \bullet \frac{255686026,1\frac{dm^{2}}{h^{2}}}{2542752000\frac{dm^{2}}{h}} = 0,185dm$$

Straty na kolankach

Metoda polega na rozwiązaniu układu równań

$\left\{ \begin{matrix} h_{3 - 5} = h^{k} + h^{L} \\ {h}_{3 - 6} = h^{k} + 2 \bullet h^{L} \\ \end{matrix} \right.\ \text{\ \ }\overset{\Rightarrow}{}\text{\ \ }\left\{ \begin{matrix} h^{k} = h_{3 - 5} - h^{L} \\ h^{L} = \frac{{h}_{3 - 6} - h^{k}}{2} \\ \end{matrix}\text{\ \ }\overset{\Rightarrow}{}\left\{ \begin{matrix} h^{k} = h_{3 - 5} - h^{L} \\ h^{L} = \frac{{h}_{3 - 6} - h_{3 - 5} + h^{L}}{2} \\ \end{matrix} \right.\ \right.\ $ $\overset{\Rightarrow}{}\left\{ \begin{matrix} h^{k} = h_{3 - 5} - h^{L} \\ h^{L} = \frac{{h}_{3 - 6} - h_{3 - 5}}{2} + \frac{h^{L}}{2} \\ \end{matrix} \right.\ \text{\ \ \ }\overset{\Rightarrow}{}\text{\ \ \ }\left\{ \begin{matrix} h^{k} = h_{3 - 5} - h^{L} \\ h^{L} = {h}_{3 - 6} - h_{3 - 5} \\ \end{matrix} \right.\ \text{\ \ \ }\overset{\Rightarrow}{}\text{\ \ }\left\{ \begin{matrix} h^{k} = (1014mm - 984mm) - h^{L} \\ h^{L} = \left( 1014mm - 962mm \right) - (1014mm - 984mm) \\ \end{matrix}\text{\ \ }{\overset{\Rightarrow}{}\text{\ \ }\left\{ \begin{matrix} h^{k} = 30mm - h^{L} \\ h^{L} = 22mm \\ \end{matrix}\text{\ \ }\overset{\Rightarrow}{}\text{\ \ }\left\{ \begin{matrix} h^{k} = 8mm \\ h^{L} = 22mm \\ \end{matrix} \right.\ \right.\ } \right.\ $

$\left\{ \begin{matrix} h_{5 - 7} = h^{k} + h^{L} \\ {h}_{3 - 7} = h^{k} + 2 \bullet h^{L} \\ \end{matrix} \right.\ \text{\ \ }\overset{\Rightarrow}{}\text{\ \ }\left\{ \begin{matrix} h^{k} = h_{5 - 7} - h^{L} \\ h^{L} = \frac{{h}_{3 - 7} - h^{k}}{2} \\ \end{matrix}\text{\ \ }\overset{\Rightarrow}{}\left\{ \begin{matrix} h^{k} = h_{5 - 7} - h^{L} \\ h^{L} = \frac{{h}_{3 - 7} - h_{5 - 7} + h^{L}}{2} \\ \end{matrix} \right.\ \right.\ $ $\overset{\Rightarrow}{}\left\{ \begin{matrix} h^{k} = h_{5 - 7} - h^{L} \\ h^{L} = \frac{{h}_{3 - 7} - h_{5 - 7}}{2} + \frac{h^{L}}{2} \\ \end{matrix} \right.\ \text{\ \ \ }\overset{\Rightarrow}{}\text{\ \ \ }\left\{ \begin{matrix} h^{k} = h_{5 - 7} - h^{L} \\ h^{L} = {h}_{3 - 7} - h_{5 - 7} \\ \end{matrix} \right.\ \text{\ \ \ }\overset{\Rightarrow}{}\text{\ \ }\left\{ \begin{matrix} h^{k} = (984mm - 952mm) - h^{L} \\ h^{L} = \left( 1001mm - 952mm \right) - (984mm - 952mm) \\ \end{matrix}\text{\ \ }{\overset{\Rightarrow}{}\text{\ \ }\left\{ \begin{matrix} h^{k} = 32mm - h^{L} \\ h^{L} = 17\text{mm} \\ \end{matrix}\text{\ \ }\overset{\Rightarrow}{}\text{\ \ }\left\{ \begin{matrix} h^{k} = 15\text{mm} \\ h^{L} = 30mm \\ \end{matrix} \right.\ \right.\ } \right.\ $