Using the given temperature and pressures, determine: a) the diameter of the water scale model balloon (m), b) the weight of the
1 answer:
Complete Question
Complete Question is attached below
Answer:
a)
b)
c)
Explanation:
From the question we are told that:
Hot air:
Temperature
Pressure
Distance
Weight
Water:
Temperature
Pressure
Since we have The same Reynolds number
a)
Generally the equation for equal Reynolds number is mathematically given by
Re_{air}=Re_{water}
Therefore
b)
Generally the equation for Weight of scale is mathematically given by
c)
Generally the equation for Density of buoyant material is mathematically given by
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(1) The position around equilibrium of an object in simple harmonic motion is described by
where
A is the amplitude of the motion
is the angular frequency.
The velocity is the derivative of the position:
where
is the maximum velocity of the object.
The acceleration is the derivative of the velocity:
where
is the maximum acceleration of the object.
We know from the problem both maximum velocity and maximum acceleration:
From the first equation, we get
(1)
and if we substitute this into the second equation, we find the angular fequency
while the amplitude is (using (1)):
(b) We found in the previous step that the angular frequency of the motion is
But the angular frequency is related to the period by
and so, the period is
where
A is the amplitude of the motion
The velocity is the derivative of the position:
where
The acceleration is the derivative of the velocity:
where
We know from the problem both maximum velocity and maximum acceleration:
From the first equation, we get
and if we substitute this into the second equation, we find the angular fequency
while the amplitude is (using (1)):
(b) We found in the previous step that the angular frequency of the motion is
But the angular frequency is related to the period by
and so, the period is