2. Prove that the maximum velocity in a circular pipe for viscous flow is equal to two times the average velocity of the flow.

Problem 5. A horizontal rough pipe with surface roughness of 1.5 × 104 m is used to transport pressurized air at a flow rate of 7 × 102 m³/s. The design guidance requires that the pressure drop must be no more than 4.2 kPa per 50 m length of the pipe. Determine the minimum diameter of the pipe

Water is being pumped the through one inch diameter piping arrangement to a higher elevation (5 meters up). Assume incompressible fluid conditions and some heat losses to the surroundings. At the inlet water pressure is 1 bar, temperature 15C, and volumetric flow rate is 0.02 m3/s. At the exit pressure is 2.2 bar, temperature is 10C and velocity of the stream is 40 m/s. Determine: a.Density of the inlet stream using NIST tables.  b.Mass flow rate [kg/s] c.Determine h2 from known p2 and T2 using NIST tables d.Find heat rate removed from Q=m(h1-h2) Use Energy Balance Equation with enthalpy difference and in the units of kW to find pumping power in kW. NOTE: The heat is removed from the system, so it should be negative in your equation! show all steps please

Water at 15°C is flowing in a 3 inch horizontal Schedule 40 steel pipe at a pressure of 102 kPa. The pipe reduces to a 1.5 inch Schedule 40 steel pipe. What is the flow rate if pressure in the 1.5 inch pipe is 99.8 kPa?