Water (γ = 62.4 lbf/ft^3) flows through a horizontal constant diameter pipe with a cross-sectional area of 8 in^2. the velocity in the pipe is 15 ft /s, and the water discharges to the atmosphere. the head loss between the pipe joint and the end of the pipe is 3ft. find the magnitude and direction of the force on the joint to hold the pipe. the pipe is mounted on frictionless rollers. assume α = 1.0 at all locations.

Awall of 0.5m thickness is to be constructed from a material which has average thermal conductivity of 1.4 w/mk. the wall is to be insulated with a material having an average thermal conductivity of 0.35 w/mk so that heat loss per square meter shall not exceed 1450 w. assume inner wall surface temperature of 1200°c and outer surface temperature of the insulation to be 15°c. calculate the thickness of insulation required.