Flow inside annular spacing is widely used in heat exchangers for various applications in thermal- fluid...

  

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Flow inside annular spacing is widely used in heat exchangers for various applications in thermal- fluid sciences. Suppose that a laminar flow condition is valid inside the annular spacing and the velocity profile within the annular spacing is defined with the following equation u(r) - Variable R. (mm) R. (mm) # (kg/ms) Ap/L. (kPa/m) Ap 4μL R² p.² + R²-R² Ro In In(R₁/Ro) This equation is valid between the inner (R) and outer radii (R) of the annular gap. Ap/L designates for the pressure drop per unit length of the pipe, stands for the viscosity of the working fluid, and r is the radial position. Consider the values given in the Table below and determine (a) The volumetric flow rate, (b) The mean velocity, (c) The maximum velocity, (d) Plot the velocity variation along with the radial position, (e) Vary the pressure drop per unit length of pipe in a selected range and plot the mean velocity as a function of Ap/L. Definition (2x (Sum of first six digits)- (Sum of last four digits)) R₂/2 (2x (Sum of first six digits)- (Sum of last four digits))/100 -5x(Sum of last four digits) Example (2020 50 80 00) 10 mm 5 mm 0.01 kg/ms -40 kPa/m Flow inside annular spacing is widely used in heat exchangers for various applications in thermal- fluid sciences. Suppose that a laminar flow condition is valid inside the annular spacing and the velocity profile within the annular spacing is defined with the following equation u(r) - Variable R. (mm) R. (mm) # (kg/ms) Ap/L. (kPa/m) Ap 4μL R² p.² + R²-R² Ro In In(R₁/Ro) This equation is valid between the inner (R) and outer radii (R) of the annular gap. Ap/L designates for the pressure drop per unit length of the pipe, stands for the viscosity of the working fluid, and r is the radial position. Consider the values given in the Table below and determine (a) The volumetric flow rate, (b) The mean velocity, (c) The maximum velocity, (d) Plot the velocity variation along with the radial position, (e) Vary the pressure drop per unit length of pipe in a selected range and plot the mean velocity as a function of Ap/L. Definition (2x (Sum of first six digits)- (Sum of last four digits)) R₂/2 (2x (Sum of first six digits)- (Sum of last four digits))/100 -5x(Sum of last four digits) Example (2020 50 80 00) 10 mm 5 mm 0.01 kg/ms -40 kPa/m

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