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Let t = sqrt(x) So dx = 2.t.dt Integrate 2 . e^t . t . dt u = 2t dv = e^t dt -> du = 2dt v = e^t -> integral(2e^t t dt) = 2 t e^t - integral(2 e^t dt) = 2 t e^t - 2 e^t = e^t (t-1) . 2 , t = sqrt_x as above

To integrate the arcsin of x, use integration by parts.

Q2. Pinch technology tutorial 1 A Network of heat exchangers is described below in data table 1. A) Produce a table showing the energy available from or required by each stream. [5 marks] B) Construct the incremental temperature–enthalpy table for the hot and cold streams. [10 marks] C) For a minimum temperature difference of 10 ˚C and the data given below construct the composite temperature enthalpy curves. [10 marks] D) Construct the shifted temperature curves. [5 marks] E) Construct the grand composite enthalpy curve and identify the pinch temperature. [5 marks] F) Determine the minimum utility heat input and the minimum heat lost to a heat sink. [5 marks] G) Use the problem table method to check your answer [15 marks] H) Determine the optimum sequence for the exchangers [15 marks] Data Table 1 Stream Number 1 2 3 4 5 6 7 Stream Enthalpy 7 2 3 8 9 2 Temperature in ºC 300 150 200 190 90 40 Temperature out ºC 150 50 50 290 190 190 PROBLEM 3. Water at 15 ˚C is fed to the top of a spray column by a centrifugal pump from a bulk storage tank at a rate of 50 kg/min. The storage tank is 15 m in diameter 3 m deep and the level within the tank is maintained at 2 m by a float valve connected to the mains water supply. The pump draws water from the bottom of the bulk storage tank at ground level and discharges it though a nozzle mounted in the roof of a spray tower 25m high. The pipes connecting the tank, pump and nozzle are all 5cm bore. The nozzle has an outlet diameter of 1 cm and is 3 cm long. The spray tower is vented to atmosphere and is drained at its base. a) Draw a diagram of this process b) The outlet velocities of the nozzles c) The pressure at the inlet of the nozzle d) The Power input by the pump assuming 100% efficiency e) The pump actually operates at 80 % efficiency, recalculate the power input to the pump.