上浒充通大￥ Shanghai Jiao Tong University 4.5 Hydrostatic Pressure Difference Between Two Points The fact that the pressure applied to a confined fluid F2=P2A2 increases the pressure FI=PA throughout the fluid by the same amount has important applications,such as in the hydraulic lifting of heavy objects: ① 分 2 B=B→ F= → F= 4 A A F
Shanghai Jiao Tong University 4.5 Hydrostatic Pressure Difference Between Two Points 12 11 1 2 12 22 F F FA P P A A FA =⇒ = ⇒ = The fact that the pressure applied to a confined fluid increases the pressure throughout the fluid by the same amount has important applications, such as in the hydraulic lifting of heavy objects:
上游充通大睾 4.6 Pressure Measurement and Manometers Shanghai Jiao Tong University 1)Piezometer tube(匀压计管) The simplest manometer is a tube,open Open at the top,which is attached to a vessel or a pipe containing liquid at a pressure (higher than atmospheric)to be measured. This simple device is known as a piezometer tube.As the tube is open to the atmosphere the pressure measured is relative to atmospheric so is gauge pressure: 卫A=Y1h This method can only be used for liquids (i.e.not for gases) and only when the liquid height is convenient to measure.It must not be too small or too large and pressure changes must be detectable
Shanghai Jiao Tong University 4.6 Pressure Measurement and Manometers 1) Piezometer tube (匀压计管) The simplest manometer is a tube, open at the top, which is attached to a vessel or a pipe containing liquid at a pressure (higher than atmospheric) to be measured. This simple device is known as a piezometer tube. As the tube is open to the atmosphere the pressure measured is relative to atmospheric so is gauge pressure: A 1 1 p = γ h This method can only be used for liquids (i.e. not for gases) and only when the liquid height is convenient to measure. It must not be too small or too large and pressure changes must be detectable
上游充通大睾 3.6 Bernoulli方程 Shanghai Jiao Tong University 如果我们考虑： 理想流体(ideal fluid,Inviscid flow); 不可压流体(constant density,incompressible flow); ● 定常流动(steady flow): 体积力为重力(gravity): 这样Lamb方程可以改写为： av D - 2 -2Vxw--bVa+r 2 +( +7(82)=2V×o
Shanghai Jiao Tong University 3.6 Bernoulli方程 ( ) 2 2 2 V p gz ρ ⎛ ⎞ ⎛ ⎞ ∇ + +∇ = × ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ∇ V ω 如果我们考虑： • 理想流体 (ideal fluid, Inviscid flow)； • 不可压流体 (constant density, incompressible flow)； • 定常流动 (steady flow)； • 体积力为重力 (gravity)； 这样Lamb方程可以改写为： 2 1 2 2 V p t ρ ∂ ⎛ ⎞ +∇ − × =− + ⎜ ⎟ ∂ ⎝ ⎠ V V ω ∇ f
上游克通大学 3.6 Bernoulli方程 Shanghai Jiao Tong University (aj-v(-vx 卫+g2 =2V×0 2 0 VH=2V×o,H= +卫+g2 2 0 这里H称为Bernoullij函数
Shanghai Jiao Tong University 3.6 Bernoulli方程 ( ) 2 2 2 V p gz ρ ⎛ ⎞ ⎛ ⎞ ∇ + +∇ = × ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ∇ V ω 2 2 2 V p gz ρ ⎛ ⎞ ∇ ++ = × ⎜ ⎟ ⎝ ⎠ V ω 这里H称为Bernoulli函数。 2 2 , 2V p H H gz ρ ∇= × = ++ V ω
上游充通大学 3.6 Bernoulliz方程 Shanghai Jiao Tong University 在流线(V)或涡线(o)上取一个微元段dl,对上式做点乘，即： 流线 VH·dl=(2V×o)dl 涡线 VH·dl=dH → dH 涡线 (2V×o)dl=0 流线 H 2 +卫+gz=C,=const 因此，Bernoullig函数在同一条流线或涡线上为常数。上式称为 Bernoulli方程(Bernoulli equation)
Shanghai Jiao Tong University 3.6 Bernoulli方程 在流线(V)或涡线(ω)上取一个微元段dl，对上式做点乘，即： ∇ H dl ⋅= × ⋅ (2V ω ) dl ( ) 0 2 0 H dl dH dH dl ∇⋅ = ⎫⎪⎬ ⇒ = V × ⋅= ω ⎪⎭ 2 const 2 l V p H gz C ρ = ++ = = 因此，Bernoulli函数在同一条流线或涡线上为常数。上式称为 Bernoulli方程(Bernoulli equation)