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 = $\frac{\pi*\ \left( 0,3m \right)^{2}}{4}$ = $\frac{3,14*0,09m^{2}}{4}$ = 0,0707

m = $\frac{F_{2}}{F_{1}}$ = $\frac{0,0707}{\ 0,1257}$ =0,5625

V₂ = $\sqrt{2g*\ \frac{1}{1 - {0,5625}^{2}}*\frac{1,2*\ 10^{5}\ \text{Pa} - 1,1*\ 10^{5}\ \text{Pa}}{9810\ \frac{N}{m^{3}}}}$ [m/s] = $\sqrt{2*9,8\ \frac{m}{s^{2}}*1,46*\ \frac{120000\ \frac{N}{m^{2}} - \ 110000\ \frac{N}{m^{2}}}{9810\ \frac{N}{m^{3}}}} = \ \sqrt{19,6\ \frac{m}{s^{2}}*1,46*1,02m} = 5,4\ \frac{m}{s}$

v₁ = m * v₂

v₁ = 0,5625 *$5,4\ \frac{m}{s}$ = 3,03 $\frac{m}{s}$

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

$$\frac{120000\frac{N}{m^{2}}}{9810\frac{N}{m^{3}}} + \ \frac{{(3,03\ \frac{m}{s})}^{2}}{2*9.8\frac{m}{s^{2}}} = \ \frac{110000\frac{N}{m^{2}}}{9810\frac{N}{m^{3}}} + \ \frac{{(5,4\frac{m}{s})}^{2}}{2*9.8\frac{m}{s^{2}}}$$

12,23+0,47=11,21+1,49

12,7=12,7

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 = $\frac{120000\ \frac{N}{m^{2}} - \ 110000\ \frac{N}{m^{2}}}{132886\frac{N}{m^{3}} - \ 9810\ \frac{N}{m^{3}}}$ = $\frac{10000\ \frac{N}{m^{2}}}{123076\frac{N}{m^{3}}}$ = 0,081m

Q = 0,96* $\frac{\pi*\ \left( 0,3m \right)^{2}}{4}$ * $\frac{1}{1 - {0,5625}^{2}}$ * $\sqrt{\frac{2*9,8\frac{m}{s^{2}}*\ 0,081m*\ (132886\frac{N}{m^{3}} - \ 9810\ \frac{N}{m^{3}})}{9810\frac{N}{m^{3}}}}$ =

0,96 * $\frac{3,14*0,09m^{2}}{4}$ * 1,46 * $\sqrt{\frac{19,6\frac{m}{s^{2}}*9969,16\ \frac{N}{m^{2}}}{9810\frac{N}{m^{3}}}}$ = 0,099 m² * $\sqrt{19,92\ \frac{m^{2}}{s^{2}}}$ = 0,099m² * 4,46 $\frac{m}{s}$ = 0,44 $\frac{m^{3}}{s}$

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 = $\sqrt{\frac{4*\ 0,44\ \frac{m^{3}}{s}}{\pi*\ 1,3\ \frac{m}{s}}}$ = 0,43m =430mm

d_srz rzeczywiste = 450mm

v_srz = $\frac{4Q}{\pi*d_{\text{srz}}^{2}}$ = $\frac{4*\ 0,44\ \frac{m^{3}}{s}}{\pi*{(0,45m)}^{2}}$ = 2,77$\frac{m}{s}$

v_srz = 2,77$\frac{m}{s}$

1. Obliczenie strat ciśnienia

1. Straty liniowe

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

ε = $\frac{1,2\text{mm}}{450\text{mm}}$ = 0,0027 ≈ 3*10^-3

Re = $\frac{2,77\frac{m}{s}*0,45m}{1,57*\ 10^{- 6}\ \frac{m^{2}}{s}}$ = 793949,04 ≈ 8 * 10⁵

λ = 0,0275

L₁ = 14m

V_srz = 2,77$\frac{m}{s}$

d_rz = 0,45m

h_strl1 = 0,0275 * $\frac{14m}{0,45m}$ * $\frac{{(2,77\frac{m}{s})}^{2}}{2*9,8\ \frac{m}{s^{2}}}$ = 0,89 * 0,39m = 0,33m

L₂ = 12m

V_srz = 2,77$\frac{m}{s}$

d_rz = 0,45m

h_strl2 = 0,0275 * $\frac{12m}{0,45m}$ * $\frac{{(2,77\frac{m}{s})}^{2}}{2*9,8\ \frac{m}{s^{2}}}$ = 0,69 * 0,39m = 0,29m

L₃ = 21m

v₁ = m * v₂

v₁ = 0,5625 *$5,4\ \frac{m}{s}$ = 3,03 $\frac{m}{s}$

d₁ = 400mm = 0,4m

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

Re = $\frac{3,03\ \frac{m}{s}*0,4m}{1,57*\ 10^{- 6}\ \frac{m^{2}}{s}}$ = 771974,52≈ 8 * 10⁵

λ = 0,028

h_strl3 = 0,028 * $\frac{21m}{0,4m}$ * $\frac{{(3,03\ \frac{m}{s})}^{2}}{2*9,8\ \frac{m}{s^{2}}}$ = 1,47 * 0,47m = 0,69m

L₄ = 10m

v₁ = 3,03 $\frac{m}{s}$

d₁ = 0,4m

h_strl4 = 0,028 * $\frac{10m}{0,4m}$ * $\frac{{(3,03\ \frac{m}{s})}^{2}}{2*9,8\ \frac{m}{s^{2}}}$ = 0,7 * 0,47m = 0,33m

L₅ = 21m

v₁ = 3,03 $\frac{m}{s}$

d₁ = 0,4m

h_strl5 = 0,028 * $\frac{21m}{0,4m}$ * $\frac{{(3,03\ \frac{m}{s})}^{2}}{2*9,8\ \frac{m}{s^{2}}}$ = 1,47 * 0,47m = 0,69m

L₆ = 390m

v₁ = 3,03 $\frac{m}{s}$

d₁ = 0,4m

h_strl6 = 0,028 * $\frac{390m}{0,4m}$ * $\frac{{(3,03\ \frac{m}{s})}^{2}}{2*9,8\ \frac{m}{s^{2}}}$ = 27,3 * 0,47m = 12,79m

L₇ = 15m

v₁ = 3,03 $\frac{m}{s}$

d₁ = 0,4m

h_strl7 = 0,028 * $\frac{15m}{0,4m}$ * $\frac{{(3,03\ \frac{m}{s})}^{2}}{2*9,8\ \frac{m}{s^{2}}}$ = 1,05 * 0,47m = 0,49m

L₈ = 4m

v₁ = 3,03 $\frac{m}{s}$

d₁ = 0,4m

h_strl8 = 0,028 * $\frac{4m}{0,4m}$ * $\frac{{(3,03\ \frac{m}{s})}^{2}}{2*9,8\ \frac{m}{s^{2}}}$ = 0,28 * 0,47m = 0,13m

L₉ = 5m

v₁ = 3,03 $\frac{m}{s}$

d₁ = 0,4m

h_strl9 = 0,028 * $\frac{5m}{0,4m}$ * $\frac{{(3,03\ \frac{m}{s})}^{2}}{2*9,8\ \frac{m}{s^{2}}}$ = 0,35 * 0,47m = 0,16m

1. Straty miejscowe

h_strM = ξ * $\frac{v^{2}}{2g}$ [m]

ξ₁ = 3,1

v₁ = $2,77\frac{m}{s}$

h_strM1 = 3,1 * $\frac{{(2,77\frac{m}{s})}^{2}}{2*9,8\frac{m}{s^{2}}}$ = 1,21 [m]

ξ₂ = 2,2

v₁ = $2,77\frac{m}{s}$

h_strM2 = 2,2 * $\frac{{(2,77\frac{m}{s})}^{2}}{2*9,8\frac{m}{s^{2}}}$ = 0,86 [m]

ξ₃ = 0,30

v₁ = $2,77\frac{m}{s}$

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 = $3,03\frac{m}{s}$

h_strM4 = 0,5 * $\frac{{(3,03\ \frac{m}{s})}^{2}}{2*9,8\frac{m}{s^{2}}}$ = 0,23 [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’= 5,4$\frac{m}{s}$– 2% (5,4$\frac{m}{s})$ = 5,292 m/s

p₁’=$\frac{({5,292\ m/s)}^{2}*\left( 1 - {0,5625}^{2} \right)*9810\frac{N}{m^{3}}}{2*9,8\frac{m}{s^{2}}}$ + 1,1*10⁵ $\frac{N}{m^{2}}$ = 2682,93 $\frac{N}{m^{2}}$ + 110000 $\frac{N}{m^{2}}$ = 112682,93 [Pa]

Δp=1,2*10⁵ [Pa] - 112682,93 [Pa] = 120000 [Pa] - 112682,93 [Pa] = 7317,07 [Pa]

h_strM5 = $\frac{p}{\gamma_{w}}$ [m]=$\ \frac{7317,07\ \lbrack N/m^{2}\rbrack}{9810\frac{N}{m^{3}}}$= 0,75 [m]

ξ₆ = 0,5

v₁ = $3,03\frac{m}{s}$

h_strM6 = 0,5 * $\frac{{(3,03\ \frac{m}{s})}^{2}}{2*9,8\frac{m}{s^{2}}}$ = 0,23 [m]

ξ₇ = 2,2

v₁ = $3,03\frac{m}{s}$

h_strM7 = 2,2 * $\frac{{(3,03\ \frac{m}{s})}^{2}}{2*9,8\frac{m}{s^{2}}}$ = 1,03 [m]

ξ₈ = 3,1

v₁ = $3,03\frac{m}{s}$

h_strM8 = 2,3 * $\frac{{(3,03\ \frac{m}{s})}^{2}}{2*9,8\frac{m}{s^{2}}}$ = 1,07 [m]

ξ₉ = 2,2

v₁ = $3,03\frac{m}{s}$

h_strM9 = 2,2 * $\frac{{(3,03\ \frac{m}{s})}^{2}}{2*9,8\frac{m}{s^{2}}}$ = 1,03 [m]

ξ₁₀ = 1

v₁ = $3,03\frac{m}{s}$

h_strM10 = 1* $\frac{{(3,03\ \frac{m}{s})}^{2}}{2*9,8\frac{m}{s^{2}}}$ = 0,47 [m]