engineeringThe deflection w of a clamped circular membrane of radius r d subjected to
pressure Pis given by (small deformation theory)
$$
w ( r ) = \frac { P r _ { d } ^ { 4 } } { 64 K } \left[ 1 - \left( \frac { r } { r _ { d } } \right) ^ { 2 } \right] ^ { 2 }
$$
where r is the radial coordinate, and $K = \frac { E t ^ { 3 } } { 12 \left( 1 - v ^ { 2 } \right) }$ , where E, t, and u are the
elastic modulus, thickness, and Poisson's ratio of the membrane, respectively. Consider a membrane with P = 15 psi, $r_d$ = 15 in., E = 18 x 10$^6$ psi,
t = 0.08 in., and $v$ = 0.3 . Make a surface plot of the membrane. engineeringNeglecting the effects of radiation absorption, emission, and scattering within their atmospheres, calculate the average temperature of Earth, Venus, and Mars assuming diffuse, gray behavior. The average distance from the sun of each of the three planets, $L_{s p}$, along with their measured average temperatures, $\bar{T}_{p}$, are shown in the table below. Based upon a comparison of the calculated and measured average temperatures, which planet is most affected by radiation transfer in its atmosphere?
$$
\begin{matrix}
\text{Planet} & \text{}{L_{s p}(\mathbf{m})} & \text{}{\bar{T}_{p}(\mathbf{K})}\\
\text{Venus} & \text{}{1.08 \times 10^{11}} & \text{735}\\
\text{Earth} & \text{}{1.50 \times 10^{11}} & \text{287}\\
\text{Mars} & \text{}{2.30 \times 10^{11}} & \text{227}\\
\end{matrix}
$$