Pressure-Momentum

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Binghamton University *

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435

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Aerospace Engineering

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Oct 30, 2023

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1 Pressure, Momentum Pressure, Momentum and Forces and Forces Consequences in Nature Consequences in Nature
2 Bernoulli Bernoulli ’ ’ s Equation s Equation Inviscid, steady flow with constant density . 2 / 2 const gz U p = + + ρ ρ along a streamline. Example consequence in Nature: Systolic pressure in the heart must be high enough to supply blood to the capillaries at the height of the brain. Most mammals have aorta blood pressure about 13,000 Pa. Giraffes have about 3X that value. Pressure changes with altitude
3 Valves in the Circulation System Valves in the Circulation System When blood flows toward the heart, the valves allow it to pass . However, if the blood starts to go the wrong way ( in small arrows ), the valves fill up and stop the backflow. Defective valves allow the pressure of an unbroken column of blood from the heart to distend blood vessels in the legs, causing varicose veins Extremities have auxiliary pumping systems. Veins are flexible and the muscles do the pumping. Valves control flow and pressure.
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4 Manometers are based on Bernoulli Inclined-tube manometers are capable of more accurate readings z g p Δ = Δ ρ
5 Flow Meter based on Bernoulli Flow Meter based on Bernoulli From Vogel, 1994 ) 1 ( 2 2 2 2 1 2 1 S S U p − = Δ ρ
6 Stagnation Pressure Stagnation Pressure
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7 Pitot* Tube to Measure Stagnation Pressure * Note that Pitot is a man’s name, so it should be capitalized
8 Difference between Stagnation and Static Pressure to Indicate Velocity, the Pitot-static Probe 2 / 2 U p ρ = Δ Measure Δ p with a manometer
9 Probes are designed so that errors in static pressure due to nose and stem cancel
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10 10 Pitot Tubes in Nature From Vogel, 1994 - Caddis fly has intake in high-pressure region and outlet in low pressure region with a filter in between. -Ascidian adds a flexible support to stay correctly oriented in tidal flows. These are expert Fluid Engineers!
11 11 Surface Pressure Distribution Surface Pressure Distribution Streamlined body (blunt nose and sharp tail) Dimensionless Pressure distribution 2 / 2 1 1 U p p C p ρ − ≡ Pressure Coefficient: From Vogel, 1994
12 12 Pressure Distributions on Fish Pressure Distributions on Fish - Gills seem to be located in regions of low pressure to aid throughflow. - Eyes seem to be located where changes in speed won’t cause pressure changes and possible distortion to the eyeball From Vogel, 1994
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13 13 Other Examples in Nature From Vogel, 1994 Prairie dogs arrange for ventilation
14 14 Forces from moving fluid on an object: (a.) pressure forces, (b.) viscous force, (c.) resultant force (lift and drag). Lift Drag Thrust
15 15 Examples from Nature Examples from Nature From Vogel, 1994
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16 16 Drag Drag This concept has been used for Drag measurements before strain gage balances. It is particularly useful in nature with complex, often flexible bodies. From Vogel, 1994 2 2 1 2 ) ( dS U U U D − = ∫∫ ρ If p 2 =p 1
17 17 Jet Propulsion Jet Propulsion Thrust from a jet is mass flow times velocity difference: ) ( 1 U U m T j − = & Power output is thrust times speed: ) ( 1 1 U U U m P j out − = & Power input is rate of kinetic energy input ) ( 2 1 2 1 2 U U m P j in − = & Propulsion Efficiency is power output over power input 1 1 2 U U U j p + = η
18 18 Jet Propulsion in Nature Jet Propulsion in Nature Just as in engineering, high propulsion efficiency requires high mass flow and low velocity difference, e.g. Turbofan From Vogel, 1994
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