Air Pressure 70 Psi

Equations

density = m/v

m = mass

v = volume

mass = d x v

d = density

v = volume

area = Pi x r2

r = radius

Drag Coefficient = 2Fd/pv2A

F = drag force

p = density

v = volume

a = area

Mass flow rate = A x cd x √(2ρΔP)

A = area

Cd = drag coefficient

p = density

ΔP = Change in pressure

Height of rocket flight = b(tan A)

b =angle of person b

a = angle of person a

ΔP = (Pi + Pf) / 2

Constants

Density of water =.998g/cm3 =998 kg/m3

Acceleration of gravity = 9.8m/s2

air pressure 70 psi

water volume 300 ml

Discharge Coefficient .98

14.7 psi = 101,353.56 N/m2

mass of water

mass = density x volume

Vol = 300 ml = 300 cm3 or 0.0003 m3

density of water = 998 kg/m3

Mass = 998 kg/m3x 0.0003 m3= 0.2994 kg H2O

mass flow rate

Average mass flow rate, ṁ, of water out of nozzle:

ṁ = A x cd x √(2ρΔP)

cd== 2Fd/pv2A

Find A of nozzle in m2: A = πr2

For diameter of ~21 cm = .021 m

Radius = d/2 = .021 m / 2 = 0.0105 m

A = π(0.0105)2 = 0.0003462 m2

Find average pressure acting on the water

ΔP = (Pi + Pf) / 2 or (Pi (1+Vi/Vf)) / 2, since PiVi = PfVf, so Pf = (PiVi)/VfPi = 70 psi

Vi of air = 2 Liter –0.3 L = 1.7 L

Vf = 2 L

Pf = 70 (1.7) / 2 = 59.5

ΔP = (70 + 59.5) / 2 = 64.75psi

Convert psi to N/m2

14.7 psi = 101,353.56 N/m2, so 64.75 psi =

101,353.56 x 64.75 / 14.7 = 446438.3 N/m2

ṁ = A x cd x √(2ρΔP)

ṁ = A x cd x √(2ρΔP)

ṁ = 0.0003462 m2 x 0.98 x (√2 x 998 kg/m3 x 446438.3 N/m2) = 18.9kg/s

Water exit velocity V = ṁ / ρA = 18.9 kg/s / (998 kg/m3)(.0003462 m2) = 54.70 m/s

Rocket thrust ft= ṁ x V = 18.9 kg/s x 54.7 m/s = 1033.83 kg m/s2or 133.83 N