Problem 9.70

กำหนดให้ \(ρ = 1,000 kg/m^{3}, y_{1} = y_{2} = 0 m, r_{1} = 2r, r_{2} = r,\)

\(P_{1} - P_{2} = 1.2\times 10^{3} Pa\) และ \(g = 9.80 m/s^{2}\)

จาก \(A_{1}v_{1} = A_{2}v_{2}\)

\(\pi r_{1}^{2}v_{1} = \pi r_{2}^{2}v_{2}\)

\(\pi (2r)^{2}v_{1} = \pi r^{2}v_{2}\)

\(v_{2} = 4v_{1}\)

จาก\(P_{1}+\frac{1}{2}ρv_{1}^{2}+ρgy_{1}=P_{2}+\frac{1}{2}ρv_{2}^{2}+ρgy_{2}\)

\(P_{1}+\frac{1}{2}ρv_{1}^{2}=P_{2}+\frac{1}{2}ρ(4v_{1})^{2}\)

\(v_{1} =\sqrt{\frac{2(P_{1} - P_{2})}{15ρ}}\)

\(v_{1} = 0.40 m/s \;\blacksquare\)