1. Obliczenie prędkości przepływu wody w przewodzie tłocznym

V₂ = $\sqrt{2g*\ \frac{1}{1 - m^{2}}*\frac{p_{1} - p_{2}}{\gamma_{w}}}$ [m/s]

Q = F₁ * v₁ = F₂ * v₂ = const

F₁ * v₁ = F₂ * v₂

v₁ = $\frac{F_{2}}{F_{1}}$ * v₂

F₁ = $\frac{\pi d_{1}^{2}}{4}$ F₁ = $\frac{\pi*{(0,4m)}^{2}}{4}$ = $\frac{3,14*0,16m^{2}}{4}$ = 0,1257

F₂ = $\frac{\pi d_{2}^{2}}{4}$ F₂ = $\frac{\pi*\ \left( 0,15m \right)^{2}}{4}$ = $\frac{3,14*0,30m^{2}}{4}$ = 0,0177

m = $\frac{F_{2}}{F_{1}}$ = $\frac{0,0707}{\ 0,1257}$ =0,1408

V₂ = $\sqrt{2g*\ \frac{1}{1 - {0,1408}^{2}}*\frac{1,9*\ 10^{5}\ \text{Pa} - 1,8*\ 10^{5}\ \text{Pa}}{9810\ \frac{N}{m^{3}}}}$ [m/s] = $\sqrt{2*9,8\ \frac{m}{s^{2}}*1,02*\ \frac{190000\ \frac{N}{m^{2}} - \ 180000\ \frac{N}{m^{2}}}{9810\ \frac{N}{m^{3}}}} = \ \sqrt{20,0\ \frac{m}{s^{2}}*1,02m} = 4,52\ \frac{m}{s}$

v₁ = m * v₂

v₁ = 0,1408 *$4,52\ \frac{m}{s}$ = 0,64 $\frac{m}{s}$

$$\frac{p_{1}}{\gamma_{w}} + \ \frac{v_{1}^{2}}{2g} = \ \frac{p_{2}}{\gamma_{w}} + \ \frac{v_{2}^{2}}{2g}$$

$$\frac{190000\frac{N}{m^{2}}}{9810\frac{N}{m^{3}}} + \ \frac{{(0,64\ \frac{m}{s})}^{2}}{2*9.8\frac{m}{s^{2}}} = \ \frac{180000\frac{N}{m^{2}}}{9810\frac{N}{m^{3}}} + \ \frac{{(4,52\frac{m}{s})}^{2}}{2*9.8\frac{m}{s^{2}}}$$

19,39=19,39

L=P

1. Obliczanie natężenia przepływu w układzie rurociągów

Q = F₂ * v₂

Q = k* $\frac{\pi d_{2}^{2}}{4}$ * $\frac{1}{1 - m^{2}}$ * $\sqrt{\frac{2g*\ H(\gamma_{\text{rt}} - \ \gamma_{w})}{\gamma_{w}}}$ [m³/s]

H = $\frac{p_{1} - p_{2}}{\gamma_{\text{rt}} - \ \gamma_{w}}$ [m]

H = $\frac{190000\ \frac{N}{m^{2}} - \ 180000\ \frac{N}{m^{2}}}{132886\frac{N}{m^{3}} - \ 9810\ \frac{N}{m^{3}}}$ = $\frac{10000\ \frac{N}{m^{2}}}{123076\frac{N}{m^{3}}}$ = 0,081m

Q = 0,96* $\frac{\pi*\ \left( 0,15m \right)^{2}}{4}$ * $\frac{1}{1 - {0,1408}^{2}}$ * $\sqrt{\frac{2*9,8\frac{m}{s^{2}}*\ 0,081m*\ (132886\frac{N}{m^{3}} - \ 9810\ \frac{N}{m^{3}})}{9810\frac{N}{m^{3}}}}$ =

0,96 * $\frac{3,14*0,0225m^{2}}{4}$ * 1,02 * $\sqrt{\frac{19,6\frac{m}{s^{2}}*9969,16\ \frac{N}{m^{2}}}{9810\frac{N}{m^{3}}}}$ = 0,020 m² * $\sqrt{19,92\ \frac{m^{2}}{s^{2}}}$ = 0,020m² * 4,46 $\frac{m}{s}$ = 0,09 $\frac{m^{3}}{s}$

1. Dobór średnicy przewodu ssawnego

d_srz = $\sqrt{\frac{4Q}{\pi*\ v_{s}}}$ [m]

v_s = 0,8 – 1,2 dla d≤ 250 mm

v_s = 1,2 – 1,5 dla d>250 mm

d_s = $\sqrt{\frac{4*\ 0,09\ \frac{m^{3}}{s}}{\pi*\ 1,4\ \frac{m}{s}}}$ = 0,28m =280mm

d_srz rzeczywiste = 300mm

v_srz = $\frac{4Q}{\pi*d_{\text{srz}}^{2}}$ = $\frac{4*\ 0,09\ \frac{m^{3}}{s}}{\pi*{(0,30m)}^{2}}$ = 1,27$\frac{m}{s}$

v_srz = 1,27$\frac{m}{s}$

1. Obliczenie strat ciśnienia

1. Straty liniowe

h_strl = λ * $\frac{L}{d}$ * $\frac{v^{2}}{2g}\ $[m]

ε = $\frac{1,2\text{mm}}{300\text{mm}}$ ≈ 4*10^-3

Re = $\frac{1,27\frac{m}{s}*0,30m}{1,57*\ 10^{- 6}\ \frac{m^{2}}{s}}$ = 242665,16≈ 2 * 10⁵

λ = 0,033

L₁ = 10m

V_srz = 1,27$\frac{m}{s}$

d_rz = 0,30m

h_strl1 = 0,033 * $\frac{10m}{0,30m}$ * $\frac{{(1,27\frac{m}{s})}^{2}}{2*9,8\ \frac{m}{s^{2}}}$ = 0,09m

L₂ = 12m

V_srz = 1,27$\frac{m}{s}$

d_rz = 0,30m

h_strl2 = 0,033 * $\frac{12m}{0,30m}$ * $\frac{{(1,27\frac{m}{s})}^{2}}{2*9,8\ \frac{m}{s^{2}}}$= 0,11m

L₃ = 17m

v₁ = m * v₂

v₁ = 0,1408 *$4,52\ \frac{m}{s}$ = 0,64 $\frac{m}{s}$

d₁ = 400mm = 0,4m

ε = $\frac{1,2\text{mm}}{400\text{mm}}$ = 0,003= 3*10^-3

Re = $\frac{0,64\ \frac{m}{s}*0,4m}{1,57*\ 10^{- 6}\ \frac{m^{2}}{s}}$ = 163057,32≈ 1 * 10⁵

λ = 0,034

h_strl3 = 0,034 * $\frac{17m}{0,4m}$ * $\frac{{(0,64\ \frac{m}{s})}^{2}}{2*9,8\ \frac{m}{s^{2}}}$ = 0,03m

L₄ = 12m

v₁ = 0,64 $\frac{m}{s}$

d₁ = 0,4m

h_strl4 = 0,034 * $\frac{12m}{0,4m}$ * $\frac{{(0,64\ \frac{m}{s})}^{2}}{2*9,8\ \frac{m}{s^{2}}}$= 0,02m

L₅ = 17m

v₁ = 0,64 $\frac{m}{s}$

d₁ = 0,4m

h_strl5 = 0,034 * $\frac{17m}{0,4m}$ * $\frac{{(0,64\ \frac{m}{s})}^{2}}{2*9,8\ \frac{m}{s^{2}}}$ = 1,47 * 0,47m = 0,03m

L₆ = 280m

v₁ = 0,64 $\frac{m}{s}$

d₁ = 0,4m

h_strl6 = 0,034 * $\frac{280m}{0,4m}$ * $\frac{{(0,64\ \frac{m}{s})}^{2}}{2*9,8\ \frac{m}{s^{2}}}$ = 0,50

L₇ = 11m

v₁ = 0,64 $\frac{m}{s}$

d₁ = 0,4m

h_strl7 = 0,034 * $\frac{11m}{0,4m}$ * $\frac{{(0,64\ \frac{m}{s})}^{2}}{2*9,8\ \frac{m}{s^{2}}}$ = 0,02m

L₈ = 7m

v₁ = 0,64 $\frac{m}{s}$

d₁ = 0,4m

h_strl8 = 0,034 * $\frac{7m}{0,4m}$ * $\frac{{(0,64\ \frac{m}{s})}^{2}}{2*9,8\ \frac{m}{s^{2}}}$ = 0,28 * 0,47m = 0,012m

L₉ = 6m

v₁ = 0,64 $\frac{m}{s}$

d₁ = 0,4m

h_strl9 = 0,034 * $\frac{6m}{0,4m}$ * $\frac{{(0,34\ \frac{m}{s})}^{2}}{2*9,8\ \frac{m}{s^{2}}}$ = 0,35 * 0,47m = 0,011m

1. Straty miejscowe

h_strM = ξ * $\frac{v^{2}}{2g}$ [m]

ξ₁ = 3,1

v₁ = $1,27\frac{m}{s}$

h_strM1 = 3,1 * $\frac{{(1,27\frac{m}{s})}^{2}}{2*9,8\frac{m}{s^{2}}}$ = 0,20 [m]

ξ₂ = 2,2

v₁ = $1,27\frac{m}{s}$

h_strM2 = 2,2 * $\frac{{(1,27\frac{m}{s})}^{2}}{2*9,8\frac{m}{s^{2}}}$ = 0,14 [m]

ξ₃ = 0,30

v₁ = $1,77\frac{m}{s}$

h_strM3 = 0,3 * $\frac{{(3,03\frac{m}{s})}^{2}}{2*9,8\frac{m}{s^{2}}}$ = 0,14 [m]

ξ₄ = 0,5

v₁ = $0,64\frac{m}{s}$

h_strM4 = 0,5 * $\frac{{(0,64\ \frac{m}{s})}^{2}}{2*9,8\frac{m}{s^{2}}}$ = 0,011 [m]

h_strM5 = $\frac{p}{\gamma_{w}}$ [m]

Δp=p₁-p₁’ [Pa]

p₁’=$\frac{v_{2}^{'2}*\left( 1 - m^{2} \right)*\gamma_{w}}{2g}$ + p₂ [Pa]

v₂’= v₂ – 2%v₂

v₂ = 5,4$\frac{m}{s}$

v₂’= 4,52$\frac{m}{s}$– 2% (4,52$\frac{m}{s})$ = 3,616 m/s

p₁’=$\frac{({3,616\ m/s)}^{2}*\left( 1 - {0,1408}^{2} \right)*9810\frac{N}{m^{3}}}{2*9,8\frac{m}{s^{2}}}$ + 1,8*10⁵ $\frac{N}{m^{2}}$ = 6414,66 $\frac{N}{m^{2}}$ + 180000 $\frac{N}{m^{2}}$ = 186414,66 [Pa]

Δp=1,9*10⁵ [Pa] - 186414,66 [Pa] = 190000 [Pa] - 186414,66 [Pa] = 3585,34 [Pa]

h_strM5 = $\frac{p}{\gamma_{w}}$ [m]=$\ \frac{3585,34\ \lbrack N/m^{2}\rbrack}{9810\frac{N}{m^{3}}}$= 0,36 [m]

ξ₆ = 0,5

v₁ = $0,64\frac{m}{s}$

h_strM6 = 0,5 * $\frac{{(0,64\ \frac{m}{s})}^{2}}{2*9,8\frac{m}{s^{2}}}$ = 0,011 [m]

ξ₇ = 2,2

v₁ = $3,03\frac{m}{s}$

h_strM7 = 2,2 * $\frac{{(0,64\ \frac{m}{s})}^{2}}{2*9,8\frac{m}{s^{2}}}$ = 0,05 [m]

ξ₈ = 3,1

v₁ = $0,64\frac{m}{s}$

h_strM8 = 3,1 * $\frac{{(0,64\ \frac{m}{s})}^{2}}{2*9,8\frac{m}{s^{2}}}$ = 0,065 [m]

ξ₉ = 2,2

v₁ = $0,64\frac{m}{s}$

h_strM9 = 2,2 * $\frac{{(0,64\ \frac{m}{s})}^{2}}{2*9,8\frac{m}{s^{2}}}$ = 0,046 [m]

ξ₁₀ = 1

v₁ = $3,03\frac{m}{s}$

h_strM10 = 1* $\frac{{(0,64\ \frac{m}{s})}^{2}}{2*9,8\frac{m}{s^{2}}}$ = 0,021 [m]