### Reverse Osmosis Desalination Process AnalysisA ground water source with a salinity (TDS) of 2850 mg/L undergoes reverse osmosis desalination to produce drinking water, resulting in a permeate with a salinity (TDS) of 200 mg/L. The feed flow rate and permeate flow rate in the membrane process are 4000 m³/d and 3200 m³/d, respectively. The resistance of the membrane \( R_m \) is \( 10^{11} \) Pa·s/m, while the driving pressure \( \Delta P \) is 10 bar. The osmotic pressure of the water can be estimated using the rule of thumb: \(\pi\) (psi) = 0.01 × TDS (mg/L).Tasks:1. Determine the required salt rejection rate of the membrane.2. Calculate the recovery of the RO process.3. Compute the permeate flux through the membrane and the necessary membrane area.4. Find the flow rate and salinity (TDS) of the concentrate flow.

NOTE: As per our policy, we can solve only the first 3 sub-parts. Given Data: The groundwater with salinity is 2850 mg/L. The permeate salinity (TDS) is cp=200 mg/L. The feed flow rate is Qf=4000 m3/d. The permeate flow rate is Qp=3200 m3/d. The resistance of the membrane is Rm=1011 Pa·s/m. The driving pressure is ∆P=10 bar. To Determine: (1): The required salt rejection rate of the membrane. (2) The recovery of the RO process. (3) The permeate flux through the membrane and the required membrane area.Part (1): The formula to calculate the salt rejection rate of the membrane is given by, Salt rejection=1-Salt passage×100...........(1) The formula to calculate the salt passage is given by, Salt passage=cpcf×100...........(2) Here, cf is the feedwater TDS. Using the overall mass equation, we know that: Qf×cf=Qp×cp+Qc×cc.............(3) Here, cc is the concentration TDS. The concentrate flow can be calculated as: Qf=Qp+Qc4000=3200+ccQc=800 m3/dSubstitute the known values in equation (3) to calculate the feedwater TDS. 4000×cf=3200×200+800×28504000×cf=2.92×106cf=730 mg/L Substitute the known values in equation (2). Salt passage=200730Salt passage=0.27 Substitute the known values in equation (1). Salt rejection=1-0.27×100Salt rejection=73%Part (2): The formula to calculate the recovery of RO process is given by, %Recovery=QpQf×100 Substitute the known values in the above formula. %Recovery=32004000×100%Recovery=80% Part (3): The formula to calculate the permeate flux through the membrane is given by, J=∆PμRm×103 Here, μ is the dynamic viscosity of water 8.90 × 10-4 Pa·s. Substitute the known values in the above formula. J=108.90×10-41011 Pa·s/m×103J=1.12×10-4 L/m2·h Hence, the required membrane area can be calculated as: J=QcAm1.12×10-4=800 m3/d×0.04166667 m3/h1 m3/dAmAm=297619.07 m2

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Civil Engineering

A ground water with salinity (TDS) of 2850 mg/L is treated with reverse osmosis desalination process for drinking water production and the permeate salinity (TDS) is measured to be 200 mg/L. The feed flow rate and permeate flow rate of the membrane process are 4000m³/d and 3200m³/d, respectively. It is known the resistance of the membrane Rm is 10¹¹ Pa-s/m and the driving pressure AP is 10 bar. The osmotic pressure of the water can be determined by the rule of thumb (psi) = 0.01TDS (mg/L). Determine (1) the required salt rejection rate of the membrane, (2) the recovery of the RO process, (3) the permeate flux through the membrane and the required membrane area, (4) the flow rate and salinity (TDS) of the concentrate flow.

A ground water with salinity (TDS) of 2850 mg/L is treated with reverse osmosis desalination process for drinking water production and the permeate salinity (TDS) is measured to be 200 mg/L. The feed flow rate and permeate flow rate of the membrane process are 4000m³/d and 3200m³/d, respectively. It is known the resistance of the membrane Rm is 10¹¹ Pa-s/m and the driving pressure AP is 10 bar. The osmotic pressure of the water can be determined by the rule of thumb (psi) = 0.01TDS (mg/L). Determine (1) the required salt rejection rate of the membrane, (2) the recovery of the RO process, (3) the permeate flux through the membrane and the required membrane area, (4) the flow rate and salinity (TDS) of the concentrate flow.

Structural Analysis

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ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

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Problem 1P

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### Reverse Osmosis Desalination Process Analysis

A ground water source with a salinity (TDS) of 2850 mg/L undergoes reverse osmosis desalination to produce drinking water, resulting in a permeate with a salinity (TDS) of 200 mg/L. The feed flow rate and permeate flow rate in the membrane process are 4000 m³/d and 3200 m³/d, respectively. The resistance of the membrane \( R_m \) is \( 10^{11} \) Pa·s/m, while the driving pressure \( \Delta P \) is 10 bar.

The osmotic pressure of the water can be estimated using the rule of thumb: \(\pi\) (psi) = 0.01 × TDS (mg/L).

Tasks:
1. Determine the required salt rejection rate of the membrane.
2. Calculate the recovery of the RO process.
3. Compute the permeate flux through the membrane and the necessary membrane area.
4. Find the flow rate and salinity (TDS) of the concentrate flow.

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