Asimple supported beam at x0 = 0 and xn = l with a uniform load w and the

vertical deflection v(x) is described by the boundary value problem

d

2

v

dx2

=

x−l

3ei

wx, v(0) = 5, v(l) = 100

where l is the length of the beam, e represents the young’s modulus of the material from which

the beam is fabricated and i is the second moment of area of the beam’s cross–section. suppose

l = 15 m, e = 210 kn/m

2

, i = 370.5 m2

and w = 9.8 kn/m. use the shooting method to

approximate the vertical deflection, v(x) with the step size, h = 3, the first guess, z0 = 10 and

the second guess, z0 = 5.

Liquid flows at steady state at a rate of 2 lb/'s through a pump, which operates to raise the elevation of the liquid 100 ft from control volume inlet to exit. the liquid specific enthalpy at the inlet is 40.09 btu/lb and at the exit is 40.94 btub. the pump requires 3 btu/s of power to operate. if kinetic energy effects are negligible and gravitational acceleration is 32.174 tt/s, the heat transfer rate associated with this steady state process is most closely 1)-2,02 btu/s from the liquid to the surroundings 2)-3.98 btu/s from the surroundings to the liquid. 3)-4.96 btu/s from the surroundings to the liquid. 4)-1.04 btu/s from the liquid to the surroundings.