Name |
Equation |
Notes |
subject
|
Acceleration of a fluid particle |
![{\displaystyle {\vec {a}}={D{\vec {V}} \over Dt}={\partial {\vec {V}} \over \partial t}+u{\partial {\vec {V}} \over \partial x}+v{\partial {\vec {V}} \over \partial y}+w{\partial {\vec {V}} \over \partial z}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3089f14a35ba9b8bb3364dce3a97ad8a32636324) |
|
Fluid Mechanics/Kinematics
|
Ideal Gas Law |
, , kJ/(kmol*K) |
|
Fluid Mechanics/Compressible Flow
|
Buoyancy force |
![{\displaystyle F_{B}=\gamma V}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c49fb642f2cadd63460a654693152b89f39a9c7d) |
V=Volume |
Fluid Statics
|
Pressure variation in motionless incompressible fluid |
![{\displaystyle p_{1}{=}\gamma h+p_{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/80e1f514831a86bf403ce0400b718f9ab078287d) |
|
Fluid Statics
|
Hydrostatic Force on plane surface |
![{\displaystyle F_{R}{=}\gamma h_{c}A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/20fe534d0ef208ce97327e9813a9bd0f0d5244d4) |
=vertical dist centroid of area |
Fluid Statics
|
Hydrostatic Force on curved surface |
![{\displaystyle x_{R}{=}{I_{s}c \over x_{c}A}+x_{c}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/187a064c8dc828a27c422699aabfef792432f94f) |
|
Fluid Statics
|
Navier-Stokes Vector form |
![{\displaystyle \rho {D{\vec {V}} \over Dt}=-{\vec {\nabla }}p+\rho {\vec {g}}+\mu \nabla ^{2}{\vec {V}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/303c1b5904209aa87c2c410c8170627824cdee1b) |
|
Fluid Mechanics/Differential Analysis of Fluid Flow
|
Navier-Stokes in x |
![{\displaystyle \rho ({\partial u \over \partial t}+u{\partial u \over \partial x}+v{\partial u \over \partial y}+w{\partial u \over \partial z})=-{\partial p \over \partial x}+\rho g_{x}+\mu ({\partial ^{2}u \over \partial x^{2}}+{\partial ^{2}u \over \partial y^{2}}+{\partial ^{2}u \over \partial z^{2}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9ec9082b7241dc3b329bd17849b46e0a15c14b93) |
|
Fluid Mechanics/Differential Analysis of Fluid Flow
|
Navier-Stokes in y |
![{\displaystyle \rho ({\partial v \over \partial t}+u{\partial v \over \partial x}+v{\partial v \over \partial y}+w{\partial v \over \partial z})=-{\partial p \over \partial y}+\rho g_{y}+\mu ({\partial ^{2}v \over \partial x^{2}}+{\partial ^{2}v \over \partial y^{2}}+{\partial ^{2}v \over \partial z^{2}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/147355dd615c1a975e91affdcd6831bd397821d3) |
|
Fluid Mechanics/Differential Analysis of Fluid Flow
|
Navier-Stokes in z |
![{\displaystyle \rho ({\partial w \over \partial t}+u{\partial w \over \partial x}+v{\partial w \over \partial y}+w{\partial w \over \partial z})=-{\partial p \over \partial z}+\rho g_{z}+\mu ({\partial ^{2}w \over \partial x^{2}}+{\partial ^{2}w \over \partial y^{2}}+{\partial ^{2}w \over \partial z^{2}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/883f143f8702a5042dfb5dfd138ac68c6f00e794) |
|
Fluid Mechanics/Differential Analysis of Fluid Flow
|
Shear Stress |
![{\displaystyle \tau =\mu {du \over dy}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dc958197c370ab35863cb1f5aaf7563cf31bc306) |
![{\displaystyle {\frac {N}{m^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5aa2b78c869d9803645d39b782c5a6de1746fc79) |
Fluid Mechanics/Analysis Methods
|
Stream Function |
and ![{\displaystyle v=-{\partial \psi \over \partial x}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5e52091e5bba052816c22340fe24924d7c6d5a15) |
|
Kinematics
|
Conservation of Mass, Steady in compressible |
![{\displaystyle \nabla {\vec {u}}={\partial u \over \partial x}+{\partial v \over \partial y}+{\partial w \over \partial z}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e0a789a1cd4f002a10adc87cb4787f9adf2bc234) |
|
Fluid Mechanics/Differential Analysis of Fluid Flow
|
Fluid Rotation |
![{\displaystyle \underbrace {{\frac {1}{2}}({\partial w \over \partial y}-{\partial v \over \partial z})} _{\omega _{x}}+\underbrace {{\frac {1}{2}}({\partial u \over \partial z}-{\partial w \over \partial x})} _{\omega _{y}}+\underbrace {{\frac {1}{2}}({\partial v \over \partial x}-{\partial u \over \partial y})} _{\omega _{z}}=\omega }](https://wikimedia.org/api/rest_v1/media/math/render/svg/1a354427259add2a760f11233c7593bd7cafefda) |
=0 if irrotational |
Fluid Mechanics/Differential Analysis of Fluid Flow
|
Streamline Flow |
![{\displaystyle Q=\psi _{B}-\psi _{A}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fd0dc076530c5db8b340434661a48598d17cfef3) |
|
Fluid Mechanics/Differential Analysis of Fluid Flow
|
Streamline |
![{\displaystyle {\frac {u}{v}}={dx \over dy}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/19b629fe42b018afcebd3ad456c98eff0883fe2c) |
|
Fluid Mechanics/Differential Analysis of Fluid Flow
|
Streakline |
![{\displaystyle {\frac {dx}{dt}}=u,{\frac {dy}{dt}}=v,{\frac {dz}{dt}}=w}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2c38a5c0d78c5adad5d518d71a73001bcf32a7af) |
|
Fluid Mechanics/Differential Analysis of Fluid Flow
|
Volumetric Dilation |
![{\displaystyle {{\vec {\nabla }}{\dot {\vec {V}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2e51918f7460578c2f06545c6756f8f142918b98) |
0 for incompressible |
Fluid Mechanics/Differential Analysis of Fluid Flow
|
Vorticity |
![{\displaystyle {\vec {\zeta }}=2{\vec {\omega }}={{\vec {\nabla }}\times {\vec {V}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5373e0636c3f61c6e7693bd83d83fd09563c4493) |
|
Fluid Mechanics/Differential Analysis of Fluid Flow
|
Specific Weight |
![{\displaystyle \gamma =\rho g}](https://wikimedia.org/api/rest_v1/media/math/render/svg/565f72d90db4ee85db6911526a3a2e3901c34b9b) |
![{\displaystyle {\frac {kg}{m^{2}s^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a6ffb7be7f4a573ff76484af6c8ee49c1777f628) |
Fluid Mechanics/Analysis Methods
|
Surface Tension |
![{\displaystyle \delta p{=}{2\sigma \over R}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ba5a28395b90f52aa5a8668ee01fe62f3f251295) |
of droplet |
Fluid Mechanics/Analysis Methods
|
Capillary Rise in Tube |
![{\displaystyle h={2\sigma \cos {\theta } \over \gamma R}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f1c58de7bf3d6e350caba324022382eb13f02fda) |
|
Fluid Mechanics/Analysis Methods
|
Torque |
![{\displaystyle dT=r\tau dA}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4ebeb60d1f8d5daa9c65a5a4fa77181f62dddff1) |
Nm |
Other
|
Streamline Coordinates |
![{\displaystyle {\vec {V}}{=}V{\hat {S}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/66667a3700dd6a3ebcd8667bddcf30d144b50b0f) |
V always tan to ![{\displaystyle {\hat {S}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/84040a3e50cb11792bdb6cfaac286b46476e3447) |
Fluid Mechanics/Analysis Methods
|
Control volume 1st law of thermodynamics |
|| || Fluid Mechanics/Control Volume Analysis
|