펌프의 입구 및 출구측에 연결된 진공계와 압력계가 각각 25 [ m m H g ] 25[mmHg] 25 [ mm H g ] 260 [ k P a ] 260[kPa] 260 [ k P a ] 0.15 [ m 3 / s ] 0.15[m^3/s] 0.15 [ m 3 / s ] [ k W ] [kW] [ kW ] 20 [ c m ] 20[cm] 20 [ c m ] 15 [ c m ] 15[cm] 15 [ c m ]
해설
입구 진공압 25 [ mmHg ] = 25 760 × 101.325 ≈ 3.33 [ kPa ] 25[\text{mmHg}]=\dfrac{25}{760}\times101.325\approx3.33[\text{kPa}] 25 [ mmHg ] = 760 25 × 101.325 ≈ 3.33 [ kPa ] 260 [ kPa ] 260[\text{kPa}] 260 [ kPa ] 260 − ( − 3.33 ) = 263.3 [ kPa ] 260-(-3.33)=263.3[\text{kPa}] 260 − ( − 3.33 ) = 263.3 [ kPa ] V 1 = Q A 1 = 0.15 π 4 ( 0.2 ) 2 ≈ 4.77 [ m/s ] V_1=\dfrac{Q}{A_1}=\dfrac{0.15}{\frac{\pi}{4}(0.2)^2}\approx4.77[\text{m/s}] V 1 = A 1 Q = 4 π ( 0.2 ) 2 0.15 ≈ 4.77 [ m/s ] V 2 = 0.15 π 4 ( 0.15 ) 2 ≈ 8.49 [ m/s ] V_2=\dfrac{0.15}{\frac{\pi}{4}(0.15)^2}\approx8.49[\text{m/s}] V 2 = 4 π ( 0.15 ) 2 0.15 ≈ 8.49 [ m/s ] ρ 2 ( V 2 2 − V 1 2 ) = 1000 2 ( 72.0 − 22.8 ) ≈ 24.6 [ kPa ] \dfrac{\rho}{2}(V_2^2-V_1^2)=\dfrac{1000}{2}(72.0-22.8)\approx24.6[\text{kPa}] 2 ρ ( V 2 2 − V 1 2 ) = 2 1000 ( 72.0 − 22.8 ) ≈ 24.6 [ kPa ] Δ p ≈ 263.3 + 24.6 = 287.9 [ kPa ] \Delta p\approx263.3+24.6=287.9[\text{kPa}] Δ p ≈ 263.3 + 24.6 = 287.9 [ kPa ] P = Q Δ p = 0.15 × 287900 ≈ 43200 [ W ] = 43.2 [ kW ] P=Q\,\Delta p=0.15\times287900\approx43200[\text{W}]=43.2[\text{kW}] P = Q Δ p = 0.15 × 287900 ≈ 43200 [ W ] = 43.2 [ kW ]
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