Given the vector current density J = (10rho2z)arho − (4rho cos2φ)aφ mA/m2 :

a. Find the current density at P (rho = 2, φ = 60◦ , z = 3);

b. Determine the total current flowing outward through the circular band rho = 4, π < φ < 2π ,

3 < z < 8.

Apiping systems consists of 6 m of 6-std type k and 12 m of 4-std type k, both drawn copper tubing. the system conveys ethylene glycol at a rate of 0.013 m3/s. the pressure drop across the system is to be calculated. there are two 90° elbows in the 6-in pipe, a reduction from the 6-in pipe to the 4-in pipe and four 90° elbows in the 4-in pipe. all fittings are soldered (same as flanged) and regular. the inlet and outlet of the system are at the same height.