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tresset_1 [31]
3 years ago
15

Consider the smoothie example given in class: Write down the production function of Tutti Frutti Smoothie example given in class

. Make sure that all ingredients are expressed in Oz. Identify the returns to scale of this production function. Is it decreasing, increasing, or constant returns to scale?
Engineering
1 answer:
mart [117]3 years ago
6 0

Answer:

Production Function : TFSq = f { ingredient 1 ...... ing. i }

Increasing/ Constant/  Increasing Returns to Scale :

Output change > / = / < Input change respectively

Explanation:

Production Function is the relationship between production inputs & outputs, given technology. It denotes the maximum output that can be generated with given inputs.

Tutti Frutti Smoothie [TFS] quantity = Function of {Ingredient1.....ingredient i}

Returns to Scale represents change in output when all inputs change in same proportion.

  • Constant Returns to Scale [CRS] : Output Change = All inputs change
  • Increasing Returns to Scale [IRS] : Output Change > All inputs change
  • Negative Returns to Scale [NRS] : Output Change < All inputs change

When all inputs (ingredients) change by same proportion i.e get twice 2X :- If output of Tutti Frutti Smoothie increases by > 2X  i.e 3X - IRS.  If it increases equal ie 2X - CRS. If it increases lesser i.e 1.5X - CRS.

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Pipe Diameter and Reynolds Number. An oil is being pumped inside a 10.0-mm-diameter pipe at a Reynolds number of 2100. The oil d
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The velocity in the pipe is 5.16m/s. The pipe diameter for the second fluid should be 6.6 mm.

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Here the first think you have to consider is the definition of the Reynolds number (Re) for flows in pipes. Rugly speaking, the Reynolds number is an adimensonal parameter to know if the fliud flow is in laminar or turbulent regime. The equation to calculate this number is:

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Now, we know that Re=2100. So the velocity is:

v=\frac{Re*\mu}{\rho*D} =\frac{2100*2.1x10^{-2}Pa*s }{855kg/m^3*0.01m} =5.16m/s

For the second fluid, we want to keep the Re=2100 and v=5.16m/s. Therefore, using the equation of Reynolds number the diameter is:

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(3) Calculate the heat flux through a sheet of brass 7.5 mm (0.30 in.) thick if the temperatures at the two faces are 150°Cand 5
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Heat flux is the rate at which thermal (heat) energy is transferred per unit surface area. It is measured in W/m2

Heat transfer(loss or gain) is unit of energy per unit time. It is measured in W or BTU/hr

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thickness, t = 7.5mm = 7.5/1000 = 0.0075m

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Heat flux, Q" = \frac{109 * 100}{0.0075} = 1,453,333.33 W/m^{2} \\ Heat flux, Q" = 1.453MW/m^{2} \\

b.) Area of sheet, A = 0.5m2

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Thermal conductivity of soda lime glass, k is approximately 1W/m.K

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Heat loss, Q = 6,666.67 * 3.41 = 22,733.33 BTU/hr

d.) Thickness, t is given as 15mm = 15/1000 = 0.015m

Heat loss, Q=\frac{109*0.5*100}{0.015} =363,333.33W

Heat loss, Q = 363,333.33 * 3.41 = 1,238,966.67 BTU/hr

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