What to submit: Either print out of a word document or A4 pages with very clean and neat handwriting 1. An oil with a viscosity of 0.40 N s m² and density 900 kg m³ flows in a 1 in Schedule 40 steel pipe (a) what is the pressure drop needed to produce a flow rate of 2x10-5 m³/s if the pipe is horizontal with a length of 10 m? (b) How steep a hill, 0, must be on if the oil is to flow through the pipe at the same rate but with no pressure drop? 2. The flow rate of corn syrup through a horizontal pipe of inner diameter 7.6 cm is monitored by measuring the pressure difference between two points of distance 1.8 m. It is proposed that Q=KAP, where the calibration constant K, is a function of temperature, T, because of the variation of the syrup's viscosity and density with temperature as shown in the table. T (°C) 15 p (kg m³) 1166 (Ns m²) 19.2 x 10-1 27 1061 9.1 x 10-1 38 1056 1.8 x 10 49 1051 2.1 x 10-2 60 1046 4.2 x 10-3 71 1041 1.1 x 10-3 (a) Plot K(T) versus T for 15°C≤T≤70°C (b) Determine the wall shear stress and the pressure drop for Q = 1.4x102 m³/s and T = 38°C (c) Determine the net pressure force, (πD2/4)Ap, and the net shear force, πDlTw, on the fluid within the pipe. 3. Air at standard conditions (p = 1.23 kg m³, µ = 1.79 x 105 N s m²) flows through a 4 mm inner diameter drawn tubing with an average velocity of V = 50 m/s. For such conditions the flow would normally be turbulent. However, if precautions are taken to eliminate the disturbances to the flow, it may be possible to obtain laminar flow. (a) Determine the pressure drop in a 0.1 m section of the tube if the flow is laminar (b) Repeat for turbulent flow