Part Of A Processing Plant Consists Of A Pipeline Which Carr

Question

Part Of A Processing Plant Consists Of a Pipeline Which Carries a Chem Part of a processing plant consists of a pipeline which carries a chemical with a relative density (to water) of 0.7. The pipeline is circular in section with a diameter which changes from 200mm at inlet to 150mm at outlet. The outlet of the pipe is 12m above that of the inlet. The pipeline is required to carry a mass flow rate of the chemical of 100kgs-1, and the pressure at the pipeline outlet must be 2bar. a) Determine the volumetric flow rate of the chemical b) Determine the velocity of the chemical at the pipeline inlet and its outlet. c) Determine the pressure required at the pipeline inlet, in bar, to achieve the desired pressure at the outlet (2 bar) I am new to this so please show all working if possible to help me better understand the process. Thank you in advance.

Dr. Jack HW Helper · Accepted Answer

Introduction The calculation of flow characteristics within pipelines carrying fluids, particularly chemicals, is fundamental in process engineering. This paper addresses the problem of determining the volumetric flow rate, velocities at different points, and the inlet pressure required to maintain specified outlet conditions for a chemical being transported through a pipeline with varying diameters and elevation. We will systematically approach the problem through fluid mechanics principles including the continuity equation, Bernoulli’s equation, and pressure head calculations. Problem Data and Parameters The fluid (chemical) has a relative density (RD) of 0.7, implying its density ($\rho$) is $0.7 \times 1000\, \text{kg/m}^3 = 700\, \text{kg/m}^3$. The inlet diameter ($D_1$) is 200 mm or 0.2 m, and the outlet diameter ($D_2$) is 150 mm or 0.15 m. The elevation difference ($\Delta z$) is 12 m, with the outlet 12 m above the inlet. The mass flow rate ($ \dot{m} $) is 100 kg/s. The required outlet pressure ($P_2$) is 2 bar, which corresponds to a gauge pressure considering atmospheric conditions. Part A: Volumetric Flow Rate ($Q$) The volumetric flow rate, $Q$, relates to mass flow rate as: $$ Q = \frac{\dot{m}}{\rho} $$ Substituting known values: $$ Q = \frac{100\, \text{kg/s}}{700\, \text{kg/m}^3} \approx 0.14286\, \text{m}^3/\text{s} $$ Thus, the volumetric flow rate of the chemical is approximately 0.143 m³/s. Part B: Velocities at Inlet and Outlet Using the cross-sectional area $A = \frac{\pi}{4} D^2$, velocities ($v$) are: $$ v = \frac{Q}{A} $$ - Inlet velocity ($v_1$): $$ A_1 = \frac{\pi}{4} \times (0.2)^2 = 0.031416\, \text{m}^2 $$ $$ v_1 = \frac{0.14286}{0.031416} \approx 4.55\, \text{m/s} $$ - Outlet velocity ($v_2$): $$ A_2 = \frac{\pi}{4} \times (0.15)^2 = 0.017671\, \text{m}^2 $$ $$ v_2 = \frac{0.14286}{0.017671} \approx 8.08\, \text{m/s} $$ The chemical velocity increases as the pipe narrows from inlet to outlet. Part C: Inlet

Part Of A Processing Plant Consists Of A Pipeline Which Carr

Part Of A Processing Plant Consists Of a Pipeline Which Carries a Chem

Paper For Above instruction

Introduction

Problem Data and Parameters

Part A: Volumetric Flow Rate (\(Q\))

Part B: Velocities at Inlet and Outlet

Part C: Inlet Pressure Calculation

Discussion and Conclusion

References