In an air heating system, heated air at 40°c and 105 kpa absolute is distributed through a 0.2 m × 0.3 m rectangular duct made of commercial steel at a rate of 0.5 m3/s. determine the pressure drop and head loss through a 30-m-long section of the duct. the roughness of commercial steel surfaces is ε = 0.45 m. the dynamic viscosity of air at 40°c is μ = 1.918 × 10–5 kg/m·s, and it is independent of pressure. the pressure drop is pa. the head loss is m.

Asolid round steel rod 6.25 mm in diameter and 375 mm long is rigidly bonded to the end of solid square brass rod 25 mm on a side and 300 mm long. the geometric axes of the bare are along the same line. an axial tensile force of 5.4 kn is applied at the extreme ends of the assembly. for steel e = 200 gpa and for brass e = 90 gpa. determine the total elongation for the assembly.

This energy transformation diagram represents the energy of a skateboarder moving along a half-pipe. as she skates toward the top of the half-pipe, her original kinetic energy is converted to potential energy and friction. how much of the energy is potential?

To understand the electric potential and electric field of a point charge in three dimensions consider a positive point charge q, located at the origin of three-dimensional space. throughout this problem, use k in place of 14? ? 0. part adue to symmetry, the electric field of a point charge at the origin must point from the origin.answer in one word.part bfind e(r), the magnitude of the electric field at distance r from the point charge q.express your answer in terms of r, k, and q. part cfind v(r), the electric potential at distance rfrom the point charge q.express your answer in terms of r, k, and q part dwhich of the following is the correct relationship between the magnitude of a radial electric field and its associated electric potential ? more than one answer may be correct for the particular case of a point charge at the origin, but you should choose the correct general relationship. a)e(r)=dv(r)drb)e(r)=v(r)rc)e(r)=? dv(r)drd)e(r)=? v(r)r