Formula Sheet Quiz #4.pdf - Mechanical Engineering...

Mechanical Engineering Department
ME 341 Belanger Spring 2021
Formula Sheet Quiz #4
Units: Force: 1 𝑁𝑁 = (1 𝑘𝑘𝑘𝑘 )(1
𝑚𝑚
𝑠𝑠
2
) , 1 𝑙𝑙𝑙𝑙𝑙𝑙 = (1 𝑠𝑠𝑙𝑙𝑠𝑠𝑘𝑘 )(1
𝑓𝑓𝑓𝑓
𝑠𝑠
2
) , 1 𝑙𝑙𝑙𝑙𝑙𝑙 = (1 𝑙𝑙𝑙𝑙𝑙𝑙
)
� 32.2
𝑓𝑓𝑓𝑓
𝑠𝑠
2
� 𝑘𝑘
𝑐𝑐
�
where
𝑘𝑘
𝑐𝑐
=
32 . 2
𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙
𝑠𝑠
2
𝑙𝑙𝑙𝑙𝑓𝑓
, 𝑘𝑘 = 9.81
𝑚𝑚
𝑠𝑠
2
= 32.2
𝑓𝑓𝑓𝑓
𝑠𝑠
2
, 1 𝑠𝑠𝑙𝑙𝑠𝑠𝑘𝑘 = 32.2 𝑙𝑙𝑙𝑙𝑙𝑙
Volume: 1 𝑙𝑙𝑓𝑓
3
= 7.48 𝑘𝑘𝑔𝑔𝑙𝑙 , 1 𝑙𝑙
3
= 1000 𝐿𝐿 , 1 𝑙𝑙𝑓𝑓
3
= 28.3 𝐿𝐿
Pressure: 1 𝑔𝑔𝑓𝑓𝑙𝑙 = 101.3 𝑘𝑘𝑘𝑘𝑔𝑔 = 14.7 𝑝𝑝𝑠𝑠𝑝𝑝 , 1 𝑘𝑘𝑔𝑔 = 1 𝑁𝑁 / 𝑙𝑙
2
Energy/Power: 1 𝑊𝑊 = 1
𝐽𝐽
𝑠𝑠
= 1
𝑁𝑁𝑚𝑚
𝑠𝑠
, 1 𝐵𝐵𝐵𝐵𝐵𝐵 = 778.17 𝑙𝑙𝑓𝑓𝑙𝑙𝑙𝑙𝑙𝑙 , 1 ℎ𝑝𝑝 = 550
𝑓𝑓𝑓𝑓𝑙𝑙𝑙𝑙𝑓𝑓
𝑠𝑠
Specific Gravity: 𝑆𝑆𝑆𝑆 =
𝜌𝜌
𝜌𝜌
𝑊𝑊𝑊𝑊𝑙𝑙𝑊𝑊𝑊𝑊
, ( 𝜌𝜌
𝑊𝑊𝑊𝑊𝑓𝑓𝑊𝑊𝑊𝑊
= 1000
𝑘𝑘𝑘𝑘
𝑚𝑚
3
= 1.94
𝑠𝑠𝑙𝑙𝑠𝑠𝑘𝑘
𝑓𝑓𝑓𝑓
3
) Specific Weight: 𝛾𝛾 = 𝜌𝜌𝑘𝑘
Ideal Gas Law:
𝑘𝑘𝑃𝑃 = 𝑙𝑙𝑚𝑚𝐵𝐵 , or 𝑘𝑘𝑃𝑃 = 𝑚𝑚𝐵𝐵 , or 𝑘𝑘 = 𝜌𝜌𝑚𝑚𝐵𝐵 ,
Viscosity: Shear Stress:
𝜏𝜏 = 𝜇𝜇
𝑑𝑑𝑠𝑠
𝑑𝑑𝑑𝑑
Kinematic Viscosity:
𝜈𝜈 =
𝜇𝜇
𝜌𝜌
Streamline and Pathline Equations: Streamline:
𝑑𝑑𝑑𝑑
𝑑𝑑𝑑𝑑
)
𝑠𝑠𝑓𝑓𝑊𝑊𝑊𝑊𝑊𝑊𝑚𝑚𝑙𝑙𝑠𝑠𝑠𝑠𝑊𝑊
=
𝑣𝑣 ( 𝑑𝑑 , 𝑑𝑑 , 𝑓𝑓 )
𝑠𝑠 ( 𝑑𝑑 , 𝑑𝑑 , 𝑓𝑓 )
Pathline:
𝑠𝑠 ( 𝑥𝑥 , 𝑦𝑦 , 𝑓𝑓 ) =
𝑑𝑑𝑑𝑑
𝑑𝑑𝑓𝑓
)
𝑝𝑝𝑊𝑊𝑊𝑊𝑓𝑓𝑠𝑠𝑐𝑐𝑙𝑙𝑊𝑊
, 𝑃𝑃 ( 𝑥𝑥 , 𝑦𝑦 , 𝑓𝑓 ) =
𝑑𝑑𝑑𝑑
𝑑𝑑𝑓𝑓
)
𝑝𝑝𝑊𝑊𝑊𝑊𝑓𝑓𝑠𝑠𝑐𝑐𝑙𝑙𝑊𝑊
Gage pressure:
𝑘𝑘
𝑘𝑘𝑊𝑊𝑘𝑘𝑊𝑊
= 𝑘𝑘
𝑊𝑊𝑙𝑙𝑠𝑠
− 𝑘𝑘
𝑊𝑊𝑓𝑓𝑚𝑚
𝑘𝑘
𝑣𝑣𝑊𝑊𝑐𝑐
= 𝑘𝑘
𝑊𝑊𝑓𝑓𝑚𝑚
− 𝑘𝑘
𝑊𝑊𝑙𝑙𝑠𝑠
Hydrostatics: Hydrostatic Equation:
−∇𝑘𝑘 + 𝜌𝜌𝑘𝑘 ⃗ = 0