Pressure Vessel, Clutches, Bearings

Question 1

Tangential Stress

Accepted Answer

$S_t=\frac{PD}{2te_j}

Question 2

Longitudinal Stress

Accepted Answer

$S_L=\frac{PD}{4te_j}

Question 3

Thickness Diameter Ratio Thin Walled

Accepted Answer

$\frac{t}{D_i}\leq 0.05$ $\frac{t}{R_i}\leq 0.1

Question 4

Spherical Thin-Walled Stress

Accepted Answer

$S=\frac{PD}{4te_j}

Question 5

Thickness Diameter Ratio Thick Wall

Accepted Answer

$\frac{t}{D_i}> 0.05$ $\frac{t}{R_i}> 0.1

Question 6

Axial Stress Thick Wall

Accepted Answer

$S_a=\frac{P_ir_i^2-P_or_o^2}{r_o^2-r_i^2}

Question 7

Radial Stress Thick Wall

Accepted Answer

$S=\frac{P_ir_i^2-P_or_o^2}{r_o^2-r_i^2}-\frac{(P_i-P_o)r_o^2r_i^2}{r_o^2-r_i^2}(\frac{1}{r^2})

Question 8

Hoop/Tangential/Circumferential Stress

Accepted Answer

$S=\frac{P_ir_i^2-P_or_o^2}{r_o^2-r_i^2}+\frac{(P_i-P_o)r_o^2r_i^2}{r_o^2-r_i^2}(\frac{1}{r^2})

Question 9

Lame's Equation (t)

Accepted Answer

$t=\frac{D_i}{2}\sqrt{\frac{S_t+P_i}{S_t-P_i}}-1

Question 10

Bach's Equation 2 formulas (t)

Accepted Answer

$t=\frac{D_i}{2}\sqrt{\frac{S_t+0.4P_i}{S_t-1.3P_i}}-1$ $t=\frac{D_i}{2}\sqrt{\frac{S_t+(1-2v)P_i}{S_t-(1+v)P_i}}-1

Question 11

Torque Friction Disk Clutchr

Accepted Answer

$T=fnF_ar_m

Question 12

Power

Accepted Answer

$P=\frac{NT}{factor}

Question 13

Uniform Wear Method (old) $r_m

Accepted Answer

$r_m=\frac{r_o+r_i}{2}$ $r_m=\frac{D_o+D_i}{4}

Question 14

Uniform Pressure Method (new) rm

Accepted Answer

$r_m=\frac{2}{3}\left[\frac{r_o^3-r_i^3}{r_o^2-r_i^2}\right]$ $r_m=\frac{1}{3}\left[\frac{D_o^3-D_i^3}{D_o^2-D_i^2}ight]

Question 15

Axial Force Clutch

Accepted Answer

$F_a=PA

Question 16

Uniform Wear Method (old) for Axial Force

Accepted Answer

$A=πDt

Question 17

Uniform Pressure Method (new) for Axial Force

Accepted Answer

$A=\frac{π}{4}(D_o^2-D_i^2)

Question 18

$Brass Tubes=T/D<0.025$ Collapsing Pressure

Accepted Answer

$P_{cr}=250,150,000\left(\frac{t}{d}ight)^3

Question 19

$Brass Tubes=T/D>0.030$ collapsing pressure

Accepted Answer

$P_{cr}=93,365\left(\frac{t}{d}ight)-2474

Question 20

Torque Cone Clutch

Accepted Answer

$T=\frac{fnF_ar_m}{sin\alpha}

Question 21

Torque Cone Engage

Accepted Answer

$T=\frac{fnF_ar_m}{sin\alpha+fcos\alpha}

Question 22

Torque Cone Disengage

Accepted Answer

$T=\frac{fnF_ar_m}{sin\alpha-fcos\alpha}

Question 23

Bearing Stress$

Accepted Answer

$S_b=\frac{F}{A_b}=\frac{F}{LD}

Question 24

Heat Radiating Capacity

Accepted Answer

$Q=\frac{Q_f}{A}=\frac{Ffv}{LD}=\frac{fF(πDN)}{LD}

Question 25

Frictional Torque Bearing

Accepted Answer

$T_f=Ffr=Ff\frac{D}{2}

Question 26

Petroff's Equation (T)

Accepted Answer

$T_f=\frac{r^3\mu N4π^2L}{C_r}$ radial clearance $C_r=C_d/2

Pressure Vessel, Clutches, Bearings

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