Fluid Dynamics

Equations

density = mass / volume

pressure = force / area = (density)(gravity)(height)

absolute pressure = atmospheric pressure + gauge pressure

Buoyant Force = (volume of fluid displaced) (density of fluid) (g)

Mass flow rate (m / t) = density (Area) (velocity)

Area1(Volume1) = Area2(Volume2)

Q = Av Volume Flow rate

P1 + rho g h + ½ rho v² = P2 + rho g h + ½ rho v²

1atm = 101 kPa = 101000 pa

density of water = 1000 kg / m³

density of oil = 900

Density is a property, changing volume or mass will not change the density

Density is set so changing 1 variable will change the other as well

Same depth same pressure, force and area will not always be the same tho

Hydraulics - pressure in = pressure out = force / area (in) = force / area (out)

F_in / A_in = F_out / A_out

When there is neutral buoyancy (an object stays at rest) it has the same density of the fluid

Specific gravity = density of object / density of water

specific gravity = rho object / pho water

Volume Displaced / Volume object = Density object / density of fluid

V displaced / V object = rho object / rho fluid

v = root 2 g (diff in h)

stream lines: closer = faster, velocity is tangent, lines never cross

Fluid Dynamics: Force proportional to pressure, lower velocity higher pressure, higher velocity lower pressure

FRQ REFLECTION

neutral buoyancy - density of object is equal to the density of fluid

Use forces to solve buoyancy problems, most of the time they will be at equilibrium meaning acceleration = 0 and forces are equal UNLESS IT SAYS SINK OR RISE

to confirm the density of an object (like to see if its real gold) solve for the buoyant force → use the buoyant force equation to solve for volume → plug into density equation

when given a percentage of volume floating use the V flu / V obj = Den obj / Den flu to solve for the objects density

free body diagrams for this unit are most of the time just W and FB with equal magnitude

be sure to include the total mass of the system when solving problems, unless it says negligable

REMEMBER TO USE KINEMATICS IT CAN BE USED TO FIND HEIGHT AND ACCELERATION

pressure will have a concave down graph with increasing height over time

ALWAYS REMEMBER TO CONNECT FORCES TO ACCELERATION AND ACCELERATION TO TIME

Bernouli’’s principal is similar to energy approach

USE FORCES AND ENERGY APROACH FOR MANY PROBLEMS SOMETIMES KINEMATICS

deriving velocity of water tank questions

similar to energy aproach

pgh = ½ p v²

gh = ½ v²

2gh = v²

root 2gh = v