If the circulation velocity in an ultrafiltration unit operation is increased, the transmembrane pressure would be required to go up so as to maintain the extent of filtration constant. An increase in the circulation velocity would essentially imply an increased circulation volumetric flow rate, which would increase the burden on the membrane to filter out the particles in lesser time, but for a larger volume of the flow. Hence the transmembrane pressure would need to be increased in order to maintain the flow and the quality of filtration. Hope this helps.
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