A liquid is entering a 10 m long pipe of 0.2 m diameter at 25°C with an average velocity of 0.02 m/s. The pipe is kept at a constant surface temperature 40°C. Assume the flow is both hydrodynamically and thermally fully-developed in the pipe. Find out the outlet temperature. Justify if the assumption of fully-developed flow is appropriate. The properties of the fluid can be assumed constant with following values Density: 484.2 kg/m³; Specific heat capacity: 2802 J/kg-K; Thermal conductivity: 0.0904 W/m.K; Dynamic viscosity: 9.197 × 10-5 kg/m-s; Prandtl number: 2.85. 29.3 ℃

Water flow in steel pipe at a temperature of 50o C as shown in the figure. The pipe is wrapped with thermal isolation. Air is flowing over the pipe at a temperature of -5o C and a speed of 3 m/sec. It is known that 1kWh costs 0.05$ Find the daily cost of the heat losses per meter without the pipe isolation? What is the daily cost saving when using the isolation?

4. Consider fully developed laminar flow in the annular space formed by two concentric cylinders with a pressure gradient, op/ax, and the inner cylinder stationary. Let r = Rand r = kR. Assuming that the velocity profile is given by u: [¹-( 7 )² + +(ma 1 R R² ap 4μ &x 1-k² In- In(1/k) R a) Obtain an expression for the location of the maximum velocity as a function of k. b) Compare the limiting case, k→ 0,with the corresponding expression for flow in a circular pipe. c) Determine the volume flow rate. d) Find an expression for the average velocity. e) Compare the limiting cases for the volume flow rate and average velocity, k →0, with the corresponding expression for flow in a circular pipe.

A fluid with a constant density of 961 kg/m3 and a constant viscosity of 1.419×10-3 Kg/m.s is flowing over a flat plate at a stream free velocity of 0.87 m/s. If the plate has a length of 2 m, answer the following: 1.What is Reynolds number at a point that is (1/4)L down the entrance?  2.Is the flow laminar or turbulent? 3.Calculate the thickness of the boundary layer in mm at (1/4)L down the entrance 4.Calculate the drag coefficient at (1/4)L down the entrance