**Exercise Set 8-55
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Tower 8-55 consists of Tower A and Tower B; a fluid flows from Tower A to Tower B due to pressure difference. The flow rate of this fluid is Vf = 14 m3/h, its density is ρ = 1000 kg/m3, and its viscosity is μ = 1×10-3 Pa·s. The pressure in Tower A is PA = 400 kPa, the total length of the pipeline is L = 20 m, the absolute roughness of the pipeline is ε = 0.3 mm, and the inner diameter of the pipeline is di = 50 mm. The local resistance in the pipeline is ΔPt = 40.2 kPa. It is now required to determine: under the above conditions, which of the following values should the pressure PB of Tower B be close to? (1) 345.8 kPa (2) 386.0 kPa (3) 182.02 kPa (4) 222.22 kPa. ε/di = 0.3/50 = 0.006; 560/Re = 560/99080 = 0.005652. Since ε/di > 560/Re, the fluid is in the turbulent rough region. The formula for λ is: λ = [1.74 – 2×log(2ε/di)] – 2 = [1.74 – 2×log(2×0.3/50)] – 2 = 0.03212. ΔPf = 0.03212×20/0.05×1000×1.9816×1.9816/2 = 252.25 kPa. 252.25 + 40.2 = 400 – PB; therefore, PB = 107.6 kPa. This is the answer I obtained. Please, expert, explain it to me.
Tower 8-55 consists of Tower A and Tower B; a fluid flows from Tower A to Tower B due to pressure difference. The flow rate of this fluid is Vf = 14 m3/h, its density is ρ = 1000 kg/m3, and its viscosity is μ = 1×10-3 Pa·s. The pressure in Tower A is PA = 400 kPa, the total length of the pipeline is L = 20 m, the absolute roughness of the pipeline is ε = 0.3 mm, and the inner diameter of the pipeline is di = 50 mm. The local resistance in the pipeline is ΔPt = 40.2 kPa. It is now required to determine: under the above conditions, which of the following values should the pressure PB of Tower B be close to? (3) 182.02 kPa
The original poster’s method is correct; they just made a simple mistake. The calculation for ΔPf should be 0.03212*20/0.05*1000*1.9816*1.9816/2 = 252.25 kPa. Moving the decimal point one place to the left will give the correct value； Additionally, the drag coefficient can be looked up in a table; simply put, the answer is 334.59