Selection calculation for security filters

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1. Under operating conditions, the water flow rate per filter element is qJ = 50 m3/h. The water inflow rate for a single reverse osmosis unit is QRJ = 174 m3/h. The number of filter elements required for one such unit is: m = QRJ / qJ = 174/50 = 3.48; therefore, 4 filter elements are used. The actual water flow rate per filter element is then 43.5 m3/h. A security filter with a diameter of 450 is used, and 4 filter elements can be installed inside the cylinder. To facilitate the replacement of the filter elements, a horizontal layout and installation method are adopted. Based on the hydraulic performance of the filter element, the maximum operating pressure drop allowed is 1 MPa; backwashing is not performed during operation. The filter element needs to be replaced when the actual operating pressure difference reaches 0.1 MPa. 2. Wall thickness calculation ● Design parameters: Operating pressure PG = 0.5 MPa; the design pressure is taken as 1.1 times the operating pressure, so PS = 1.1 × 0.5 = 0.55 MPa. The calculated pressure PC = PS + 0.1 = 0.65 MPa. The test pressure is 1.25 times the design pressure, resulting in PJ = 1.25 × 0.55 = 0.6875 ≈ 0.7 MPa ； The inner diameter of the filter, Di = 450 mm. When the operating temperature is ≤100°C, the allowable stress for stainless steel [σ] = 137 MPa. No non-destructive testing is required, and the weld coefficient for single-face butt welding is φ = 0.6 ； ● Calculated wall thickness of the cylinder: S0 = PC·DI / (2[σ]φ – PC) = 0.65×450 / (2×137×0.6 – 0.65) = 1.786 ≈ 1.8 mm. Additional wall thickness: For steel plates with a thickness of 2 mm or less, the negative deviation C1 is 0.18 mm ； The thickness reduction C2 of cold-rolled cylindrical steel plates is 0, and the corrosion margin of ultrafiltration effluent against stainless steel is C3 = 1 mm. The additional wall thickness for the container, C′ = C1 + C3 = 0.18 + 1 = 1.18 mm. The wall thickness of the filter cylinder is: S1 = S0 + C′ = 1.8 + 1.18 = 2.98 mm. To meet a working pressure of 0.5 MPa and satisfy the stiffness requirement that the minimum wall thickness of the 400 stainless steel container should be at least 3 mm, S1 is set to 3 mm. ● Wall thickness calculation for the head: Using a standard elliptical head, the wall thickness is calculated as follows: S0′ = PC Di / (2[σ]φ – 0.5PC) = 0.65×450 / (2×137×0.6 – 0.5×0.65) = 1.783 ≈ 1.8 mm. The thickness reduction of the steel plate used for the heat-pressed head is 10% of the calculated wall thickness; thus, C2 = 0.1S0′ = 0.1×1.8 = 0.18 mm. The additional thickness for the head’s wall is given by C″ = C1 + C2 + C3 = 0.18 + 0.18 + 1 = 1.36 mm. The wall thickness of the filter head is S2 = S0′ + C″ = 1.8 + 1.36 = 3.16 mm; therefore, S2 is taken as 3.5 mm. ● For easy replacement of the filter elements, the safety filter is installed horizontally; it features a vertically suspended rotary design with flanged end caps. Its total length is 1500 mm, and the center height of the filter cartridge is 915 mm. ● For the process pipe connections, the water flow velocity inside the inlet and outlet pipes is u = 1.5 m/s, and the water flow rate is Q_RJ = 174 m³/h. The diameter of the inlet and outlet pipes is given by d = 18.8 × (Q/u)⁰·⁵; calculating this yields d = 18.8 × (174/1.5)⁰·⁵ = 202.48 mm. Therefore, d is taken as DN200.