$$2\overset{\overline{}}{r} = 3,706\ \rightarrow \ \overset{\overline{}}{r} = 1,853$$
$\overset{\overline{}}{t} = 2,141\ s$ l = 60cm
$$\eta = \frac{2r^{2} \bullet t}{9 \bullet l} \bullet \left( \rho_{k} - \rho_{c} \right) \bullet g = \ \frac{2 \bullet \left( 1,853 \bullet 10^{- 3} \right)^{2} \bullet 2,141}{9 \bullet 0,6} \bullet \left( 11370 - 1250 \right) \bullet 9,81 = 0,2703044912\ \approx 0,270\ \frac{\text{kg}}{m \bullet s}$$
$$\frac{\mathbf{m}^{\mathbf{2}}\mathbf{\bullet s}}{\mathbf{m}}\mathbf{\bullet}\frac{\mathbf{\text{kg}}}{\mathbf{m}^{\mathbf{3}}}\mathbf{\bullet}\frac{\mathbf{m}}{\mathbf{s}^{\mathbf{2}}}\mathbf{=}\frac{\mathbf{\text{kg}}}{\mathbf{m \bullet s}}$$
$$2\overset{\overline{}}{r} - 2r_{1}$$ |
|
---|---|
ε1 = 0, 456 |
ε21 = 0, 207936 |
ε2 = −0, 244 |
ε22 = 0, 059536 |
ε3 = −0, 394 |
ε23 = 0, 155236 |
ε4 = 0, 066 |
ε24 = 0, 004356 |
ε5 = 0, 006 |
ε25 = 0, 000036 |
ε6 = −0, 244 |
ε26 = 0, 059536 |
ε7 = 0, 606 |
ε27 = 0, 367236 |
ε8 = 0, 336 |
ε28 = 0, 112896 |
ε9 = −0, 094 |
ε29 = 0, 008836 |
ε10 = −0, 494 |
ε210 = 0, 244036 |
$$\sum_{i = 1}^{10}{\varepsilon i^{2} = 1,21964}$$
$$U_{A}\left( 2r \right) = \ \sqrt{\frac{\sum_{}^{}{\varepsilon^{2}}_{i}}{n\left( n - 1 \right)} =}\sqrt{\frac{1,21964}{90} =}0,116411mm$$
$$U_{B}\left( 2r \right) = \ \frac{2r}{\sqrt{3}} = \frac{0,01}{\sqrt{3}} = 0,005774mm$$
$$U_{c}\left( 2r \right) = \sqrt{{U^{2}}_{A} + {U^{2}}_{B}} = \ \sqrt{\left( 0,116411 \right)^{2} + \left( 0,005774 \right)^{2}} = = 0,116554mm$$
$$U_{c}\left( r \right) = \ \frac{1}{2}U_{c}\left( 2r \right) = \frac{1}{2} \bullet 0,116554 = 0,058277mm = 0,058277 \bullet 10^{- 3}m = 5,8277 \bullet 10^{- 5}m$$
$$\overset{\overline{}}{t} - t_{1}$$ |
|
---|---|
ε1 = −0, 169 |
ε21 = 0, 028561 |
ε2 = −0, 049 |
ε22 = 0, 002401 |
ε3 = 0, 081 |
ε23 = 0, 006561 |
ε4 = 0, 101 |
ε24 = 0, 010201 |
ε5 = −0, 009 |
ε25 = 0, 000081 |
ε6 = 0, 141 |
ε26 = 0, 019881 |
ε7 = −0, 109 |
ε27 = 0, 006241 |
ε8 = −0, 079 |
ε28 = 0, 006241 |
ε9 = −0, 019 |
ε29 = 0, 000361 |
ε10 = 0, 111 |
ε210 = 0, 012321 |
$$\sum_{i = 1}^{10}{\varepsilon i^{2} = 0,09285}$$
$$U_{A}\left( 2r \right) = \ \sqrt{\frac{\sum_{}^{}{\varepsilon^{2}}_{i}}{n\left( n - 1 \right)} =}\sqrt{\frac{0,09285}{90} =}0,032119s$$
$$U_{B}\left( 2r \right) = \ \frac{2r}{\sqrt{3}} = \frac{0,01}{\sqrt{3}} = 0,115470s$$
$$U_{c}\left( 2r \right) = \sqrt{{U^{2}}_{A} + {U^{2}}_{B}} = \ \sqrt{\left( 0,032119 \right)^{2} + \left( 0,115470 \right)^{2}} = 0,119853s$$
$$U_{C}\left( l \right) = U_{B}\left( l \right) = \frac{l}{\sqrt{3}} = \frac{1}{\sqrt{3}} = 0,5774mm = 0,5774 \bullet 10^{- 3}m = 5,774 \bullet 10^{- 4}m$$
$$\frac{\mathbf{\partial\eta}}{\mathbf{\partial r}}\mathbf{=}\frac{\mathbf{2}\mathbf{l}}{\mathbf{9}\mathbf{l}}\left( \mathbf{\rho}_{\mathbf{k}}\mathbf{-}\mathbf{\rho}_{\mathbf{c}} \right)\frac{\mathbf{\partial}}{\mathbf{\partial r}}\left( \mathbf{r}^{\mathbf{2}} \right)\mathbf{=}\frac{\mathbf{2 \bullet 2}\mathbf{r \bullet t}}{\mathbf{9}\mathbf{l}}\mathbf{(}\mathbf{\rho}_{\mathbf{k}}\mathbf{-}\mathbf{\rho}_{\mathbf{c}}\mathbf{) \bullet g}$$
$$\frac{\partial\eta}{\partial r} = \frac{4rt}{9l}\left( \rho_{c} - \rho_{k} \right) \bullet g = \frac{4 \bullet 1,853 \bullet 10^{- 3} \bullet 2,141}{5,4} \bullet \left( 11370 - 1250 \right) \bullet 9,81 = 291,7479667 = 2,917479 \bullet 10^{2}$$
$$\left( \frac{\partial\eta}{\partial r} \right)^{2} = 85116,83715 = 8,511683 \bullet 10^{4}$$
$$\frac{\partial\eta}{\partial t} = \frac{2r^{2}}{9l}\left( \rho_{c} - \rho_{k} \right) \bullet g = \frac{2\left( 1,853 \bullet 10^{- 3} \right)^{2}}{5,4} \bullet \left( 11370 - 1250 \right) \bullet 9,81 = 0,1262515139 = 1,262515 \bullet 10^{- 1}$$
$$\left( \frac{\partial\eta}{\partial t} \right)^{2} = 0,01593944 = 1,593944 \bullet 10^{- 2}$$
$$\frac{\partial\eta}{\partial l} = \frac{2r^{2} \bullet t}{9l^{2}}\left( \rho_{c} - \rho_{k} \right) \bullet g = \frac{2\left( 1,853 \bullet 10^{- 3} \right)^{2} \bullet 2,141}{3,24} \bullet \left( 11370 - 1250 \right) \bullet 9,81 = 0,450507 = 4,50507 \bullet 10^{- 1}$$
$$\left( \frac{\partial\eta}{\partial l} \right)^{2} = 0,202956 = 2,02956 \bullet 10^{- 1}$$
U2C(r) = 3, 396208 • 10−9
U2C(l) = 3, 333907 • 10−7
U2C(t) = 0, 01436474161 = 1, 436474 • 10−2
$$U_{c}\left( \eta \right) = \sqrt{\left( \frac{\partial\eta}{\partial r} \right)^{2} \bullet {U^{2}}_{c}\left( r \right) + \left( \frac{\partial\eta}{\partial l} \right)^{2} \bullet {U^{2}}_{c}\left( l \right) + \left( \frac{\partial\eta}{\partial t} \right)^{2} \bullet {U^{2}}_{c}\left( t \right) =} = \sqrt{8,511683 \bullet 10^{4} \bullet 3,396208 \bullet 10^{- 9} + 2,02956 \bullet 10^{- 1} \bullet 3,333907 \bullet 10^{- 7} + 1,593944 \bullet 10^{- 2} \bullet 1,436474 \bullet 10^{- 2}} = \sqrt{2,89074459 \bullet 10^{- 4} + 6,76636429 \bullet 10^{- 8} + 2,2896591 \bullet 10^{- 4}} = \sqrt{5,181080326 \bullet 10^{- 4}} = 0,02276198657 = 2,276198 \bullet 10^{- 2} = 0,02276198657 \approx 0,023\ \frac{\text{kg}}{m \bullet s}\ $$
$$\eta = (0,270 \pm 0,023)\frac{\text{kg}}{m \bullet s}\ $$