Aspherical hot-air balloon is initially filled with air at 120 kpa and 20°c with an initial diameter of 5 m. air enters this balloon at 120 kpa and 20°c with a velocity of 3 m/s through a 1-m-diameter opening. how many minutes will it take to inflate this balloon to a 17-m diameter when the pressure and temperature of the air in the balloon remain the same as the air entering the balloon?

  t = 1064 s

Explanation:

This exercise will work with the equations of fluid mechanics, let's start by calculating the filling flow rate

       Q = A v

Area of the circle is

        r = d / 2 = 0.50 m

        A = π R²

        A = π 0.50²

       A = 0.785 m²

       Q = 0.785 3

       Q = 2,356 m · / s

Let's calculate the initial and final volume

       Ro = 5/2 m = 2.5 m

       Rf = 17/2 m = 8.5 m

      V = 4/3 π r³

      Vo = 4/3 π 2.5³

      Vo = 65.45 m³

      Vf = 4/3 π 8.5³

      Vf = 2572.44 m³

The difference is the volume to be filled  

     ΔV = Vf - Vo

     ΔV = 2572.44 - 65.45

     ΔV = 2506.99 m3

As we have the flow, let's calculate the time

     Q = V / t

     t = V / Q

     t = 2506.99 / 2,356

     t = 1064 s

the independent variable, the one that is intentionally manipulated, is whether or not the car hits the barrier.

the dependent variable, the one that you measure the response in, is the distance that the washers travel.