Question
Create a C++ program with if, else and cycle Explanation of Option B - Resistance force or drag of a fluid on a sphere Any
Create a C++ program with if, else and cycle
Explanation of Option B - Resistance force or drag of a fluid on a sphere
Any object that moves through a fluid (a gas or liquid) experiences a force that
brakes called "drag" or resistance force. The "drag" is then the resistance imposed by a fluid to the
movement of an object. The resistance force or "drag" is calculated with the following formula:
= CApv^2
Where:
F = Resistance force or "drag", in newtons
C = Coefficient of resistance (dimensionless)
A = Projected frontal area of the object (m2)
- For a sphere the projected frontal area is:
=
p = fluid density (kg / m3)
v = velocity of the object relative to the fluid (m / s)
The coefficient of resistance, C, is usually measured experimentally. It is usually expressed as a
function of the Reynolds number (something that is studied in the fluid class), defined as:
= pLv
Where,
p = fluid density (kg / m3
)
L = a characteristic length of the object (such as its diameter, m)
v = velocity of the object (m / s)
= the viscosity of the fluid (Pa s)
According to C. Chow (An Introduction to Computational Fluid Mechanics, Wiley, 1979), the coefficient of
Resistance for a sphere can be approximated as follows, depending on the value of the Number of
Reynolds, Re
Reynolds number value, Re | Coefficient of resistance, C |
Re 1 | C = 24 Re- 1 |
1 < Re 400 | C = 24 Re^- 0.646 |
400 < Re 3 x 10^5 (o sea, 300,000) | C = 0.5 |
300000 < Re 2 x 10^6 (o sea, 2,000,000) | C = 0.000366 Re^0.4275 |
2000000 < Re | C = 0.18 |
Note: To raise a base to an exponent, C ++ does not have an operator but uses a function called pow, found in themath library. This function is provided with the basis and exponent, separated by commas, inside parentheses. For example, to raise Re to the power -0.646, this is expressed in C ++ as: pow (Re, -0.646). You must place the math library at the top of the program below , as follows: #include Write a program that calculates the resistance force, F, on a sphere, given the following data: 1) the diameter of the sphere (L), 2) its speed (v), 3) the density (p) of the fluid, and 4) the viscosity () of the fluid It is expected to validate all input data using a cyclic instruction.
Numerical example Assuming we have: -A sphere with diameter L = 0.21 m (eg a volleyball) -Air density (fluid) p = 1.09 kg / m3 (at 50 degrees Celsius temperature) -Air viscosity (fluid) = 1.95 10-5 Pa s = 0.0000195 Pa s (at 50 degrees Celsius temperature) -Object speed (sphere), v = 5 m / s Calculations: = = (1.09) (0.21) (5) (0.0000195) = 58,692.3077 Looking at the table above we notice that as the Raynolds number, Re, falls in the range 400 The projected frontal area of the sphere is: = 2 = ( 2 ) 2 = 3.1416 ( 0.21 2 ) 2 = 0.03463614 2 and the resistance force, F, would be: = one 2 2 = one 2 (0.5) (0.03463614) (1.09) (5) 2 = 0.2359587 Display output sample - Option B (using the data from the previous example) Your program is expected to print a report with the information organized as follows (this being presents is only the output that option B generates, but the input part that you precedes: |
ou selected option B - Resistance force or "drag" of a fluid on a sphere Enter the diameter of the sphere (in meters): 0.21 Between object speed (m / s): 5 Between fluid density (kg / m ^ 3): 1.09 Between fluid viscosity (Pa s): 0.0000195 REPORT OF RESISTANCE FORCE OF A FLUID ON A SPHERE Reynolds number: 58692.3077 Coefficient of Resistance: 0.5 Sphere Projected Frontal Area: 0.03463614 m ^ 2 Resistance Force *: 0.2359587 N -------------------------------------------------- -------------- * Corresponds to the following data: Diameter Density Viscosity Speed Sphere Fluid Fluid Object 0.21 m 1.09 kg / m ^ 3 0.0000195 Pa s 5 m / s
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