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Physics 108 lecture 8: Fluid Dynamics

2. Example (continuity): Your garden hose is about 1.0cm in radius. If water flows at 1.0m/s through the hose and reaches a nozzle of radius 1.5mm, what is the velocity coming out the nozzle? . Given??????????????????? Path?????????????????? Want?????????? Conversions/Equations. 3. Bernoulli's equa

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Physics 108 lecture 8: Fluid Dynamics

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    1. 1 Physics 108 – lecture 8: Fluid Dynamics Fluid dynamics is the study of how flowing fluids behave.   An ideal flowing fluid is steady state (motion at any one location not changing) irrotational (fluid not rotating around direction of flow) nonviscous (no friction internally or on walls) imcompressible (density is constant)   Mass flow rate: relates to area, velocity, and density:   why:   The equation of continuity: mass going in equals mass coming out why:    

    2. 2 Example (continuity): Your garden hose is about 1.0cm in radius. If water flows at 1.0m/s through the hose and reaches a nozzle of radius 1.5mm, what is the velocity coming out the nozzle?

    3. 3 Bernoulli’s equation energy is conserved for a flowing fluid (see book derivation)     P1,2 = pressure at pts 1,2 v1,2 = speed at pts 1,2 y1,2 = height at pts 1,2 = fluid density g = gravity Think Pair Share Task: what would happen above if someone: squeezed the bag: uncoiled the hose and put the bag higher:

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    5. 5 What is Viscosity? Viscosity (?)- internal resistance to flow within a fluid. Viscosity can be thought of as a measure of the “thickness” of a fluid. Higher viscosity means higher resistance to flow. The units of viscosity are Poiseuilles (Pl) , or centipoise (cP): [Pl] = [Pa][s] and 1[cP] = 0.01[Pl]   Poiseuille’s law Poieseuillés law relates how much volume of fluid per amount of time can be forced through a tube. This is called a volume flow rate and is related to the: viscosity of the fluid (higher viscosity ? lower flow rate) pressure difference on the tube ends (greater pressure ? higher flow rate) geometry of the tube (larger radius and shorter length ? higher flow rate)  

    6. 6 Example (viscosity):Blood flows into a dialysis machine through a 1.3mm diameter tube of length 2m. The pressure driving the flow equals the patient’s 50mmHg blood pressure. What volume of blood is processed in 1 hour by the machine?

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