A thick steel slab ( ρ = 7800 kg/m 3 , c = 480 J/kg ⋅ K, k = 50 W/m ⋅ K ) is initially at 300 ° C and is cooled by water jets impinging on one of its surfaces. The temperature of the water is 25 ° C, and the jets maintain an extremely large, approximately uniform convection coefficient at the surface. Assuming that the surface is maintained at the temperature of the water throughout the cooling, how long will it take for the temperature to reach 50 ° C at a distance of 25 mm from the surface?
A thick steel slab ( ρ = 7800 kg/m 3 , c = 480 J/kg ⋅ K, k = 50 W/m ⋅ K ) is initially at 300 ° C and is cooled by water jets impinging on one of its surfaces. The temperature of the water is 25 ° C, and the jets maintain an extremely large, approximately uniform convection coefficient at the surface. Assuming that the surface is maintained at the temperature of the water throughout the cooling, how long will it take for the temperature to reach 50 ° C at a distance of 25 mm from the surface?
Solution Summary: The author explains how the energy removed from the pavement for a 30-minute time period will take 1793 seconds for the temperature to reach 50 o C.
A thick steel slab
(
ρ
=
7800
kg/m
3
,
c
=
480
J/kg
⋅
K,
k
=
50
W/m
⋅
K
)
is initially at
300
°
C
and is cooled by water jets impinging on one of its surfaces. The temperature of the water is
25
°
C,
and the jets maintain an extremely large, approximately uniform convection coefficient at the surface. Assuming that the surface is maintained at the temperature of the water throughout the cooling, how long will it take for the temperature to reach
50
°
C
at a distance of 25 mm from the surface?
Assume a Space Launch System (Figure 1(a)) that is approximated as a cantilever undamped single degree of freedom (SDOF) system with a mass at its free end (Figure 1(b)). The cantilever is assumed to be massless. Assume a wind load that is approximated with a concentrated harmonic forcing function p(t) = posin(ωt) acting on the mass. The known properties of the SDOF and the applied forcing function are given below. • Mass of SDOF: m =120 kip/g • Acceleration of gravity: g = 386 in/sec2 • Bending sectional stiffness of SDOF: EI = 1015 lbf×in2 • Height of SDOF: h = 2000 inches • Amplitude of forcing function: po = 6 kip • Forcing frequency: f = 8 H
Assume a Space Launch System (Figure 1(a)) that is approximated as a cantilever undamped single degree of freedom (SDOF) system with a mass at its free end (Figure 1(b)). The cantilever is assumed to be massless. Assume a wind load that is approximated with a concentrated harmonic forcing function p(t) = posin(ωt) acting on the mass. The known properties of the SDOF and the applied forcing function are given below. • Mass of SDOF: m =120 kip/g • Acceleration of gravity: g = 386 in/sec2 • Bending sectional stiffness of SDOF: EI = 1015 lbf×in2 • Height of SDOF: h = 2000 inches • Amplitude of forcing function: po = 6 kip • Forcing frequency: f = 8 Hz Figure 1: Single-degree-of-freedom system in Problem 1. Please compute the following considering the steady-state response of the SDOF system. Do not consider the transient response unless it is explicitly stated in the question. (a) The natural circular frequency and the natural period of the SDOF. (10 points) (b) The maximum displacement of…
Assume a Space Launch System (Figure 1(a)) that is approximated as a cantilever undamped single degree of freedom (SDOF) system with a mass at its free end (Figure 1(b)). The cantilever is assumed to be massless. Assume a wind load that is approximated with a concentrated harmonic forcing function p(t) = posin(ωt) acting on the mass. The known properties of the SDOF and the applied forcing function are given below. • Mass of SDOF: m =120 kip/g • Acceleration of gravity: g = 386 in/sec2 • Bending sectional stiffness of SDOF: EI = 1015 lbf×in2 • Height of SDOF: h = 2000 inches • Amplitude of forcing function: po = 6 kip • Forcing frequency: f = 8 Hz Figure 1: Single-degree-of-freedom system in Problem 1. Please compute the following considering the steady-state response of the SDOF system. Do not consider the transient response unless it is explicitly stated in the question. (a) The natural circular frequency and the natural period of the SDOF. (10 points) (b) The maximum displacement of…
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