Question

Using the given temperature and pressures, determine: a) the diameter of the water scale model balloon (m), b) the weight of the scale model, c) the specific gravity of the buoyant material such that the model conditions will be similar to the full-scale balloon.

Answer 1

Complete Question

Complete Question is attached below

Answer:

a)
`D=0.7`

b)
`W=1787.5N`

c)
`\rho'=998.19kg/m^3`

Step-by-step explanation:

From the question we are told that:

Hot air:

Temperature
`T_a=360K`

Pressure
`P_a=100kPa`

Distance
`d=12m`

Weight
`W=1400N`

Water:

Temperature
`T_w=300K`

Pressure
`P_w=100kPa`

Since we have The same Reynolds number

a)

Generally the equation for equal Reynolds number is mathematically given by

Re_{air}=Re_{water}

Therefore

`(\rho V D)/(\mu_(air))=(p_(water)*V*D)/(\mu_(water]))`

`(100*12)/(300*0.28*1.81*10^(-3))}=(998*D)/(0.000890)`

`D=0.7`

b)

Generally the equation for Weight of scale is mathematically given by

`W=\rho*V*g`

`W=998*(4)/(3)*\pi*0.35^3*9.81`

`W=1787.5N`

c)

Generally the equation for Density of buoyant material is mathematically given by

`\rho'=(w)/(g*V)`

`\rho'=(1781.5)/((4)/(3)*\pi*0.35^3*9.81)`

`\rho'=998.19kg/m^3`