It is desired to produce and aligned carbon fiber-epoxy matrix composite having a longitudinal tensile strength of 600 MPa. Calculate (a) the critical fiber length, and (b) the volume fraction of fibers necessary if (1) the average fiber diameter is 0.028 mm, (2) the average fiber length is 2.2 mm, (3) the fiber fracture strength is 5000 MPa, (4) the fiber-matrix bond strength is 19 MPa, (5) the matrix stress at fiber failure is 16.0 MPa.

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.