System Dynamics
3rd Edition
ISBN: 9780077509125
Author: Palm
Publisher: MCG
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Chapter 1, Problem 1.22P
The flow rate f in
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Using Newton's second law, the movement of a body in a viscous fluid can be modeled. For this case it will be a one-dimensional movement.
ec.1) F -FR = ma
F: Force applied to the body.
FR: Resistance that opposes the fluid to the movement.
m: body mass
a: body acceleration
For a sphere with initial radius R0 = 1 meter and density 8960 kg/m^3 to which a constant force of 3 Kilo Newtons is applied, it is requested:
Using Euler's method, find the velocity as a function of time for the first 5 seconds of movement, considering that v(0) = 10 m/s. Use a 1 second step.
For this case use:
ec.2) FR = 210Rv
R: Radius of the sphere.
v: velocity
Where, in addition, the sphere disintegrates as time passes in this fluid, so its radius is given by the following function:
ec.3) R = R0*e^(-t/250)
A boundary layer is a thin region (usually along a wall)in which viscous forces are significant and within which the flow is rotational. Consider a boundary layer growing along a thin flat plate. The flow is steady. The boundary layer thickness d (m) at any downstream distance x is a function of x (m), free-stream velocity V(m/s)`, fluid properties fluid density r (kg/m3), fluid viscosity µ (kg/m.s), sound velocity c (m/s) and surface roughness ɛ (m).
i-Use the method of repeating variables to generate a dimensionless relationship between boundary layer thickness d (m) and other parameters. Show all your work in detail.
ii-calculate the boundary layer thickness d (m) value for x=16,2 m, free-stream velocity V=262 (m/s), fluid properties fluid density r=1.162 (kg/m3), fluid viscosity µ=1.862 x10-5 (kg/m.s), sound velocity c=345 (m/s) and surface roughness ɛ=0.015m (m). What should the velocity of wind tunnel test the similar in wind tunnel at the same temperature and pressure for…
The volume flow Q over a certain dam is a function of damwidth b , gravity g , and the upstream water depth H abovethe dam crest. It is known that Q is proportional to b . If b=120 ft and H =15 in., the flow rate is 600 ft 3 /s. What willbe the flow rate if H = 3 ft?
Chapter 1 Solutions
System Dynamics
Ch. 1 - Prob. 1.1PCh. 1 - Folklore has it that Sir Isaac Newton formulated...Ch. 1 - A ball is thrown a distance of 50 feet. 5 inches....Ch. 1 - An American football field is 100 yards long. How...Ch. 1 - How long is a 100-meter dash in feet?Ch. 1 - Convert 50 feet per second to miles per hour.Ch. 1 - The speed limit in some countries is 100...Ch. 1 - How many 60 watt lightbulbs are equivalent to one...Ch. 1 - Convert the temperature of 70°F to °C.Ch. 1 - Convert 30°C to °F.
Ch. 1 - A particular motor rotates at 3000 revolutions per...Ch. 1 - The displacement of a certain object is described...Ch. 1 - Prob. 1.13PCh. 1 - The displacement in meters of a certain vibrating...Ch. 1 - The distance a spring stretches from its “free...Ch. 1 - The following “small angle” approximation for the...Ch. 1 - Prob. 1.17PCh. 1 - Obtain two linear approximations of the function...Ch. 1 - Prob. 1.19PCh. 1 - Obtain two linear approximations of the function...Ch. 1 - Obtain a linear approximation of the function fh=h...Ch. 1 - The flow rate f in m3/s of water through a...Ch. 1 - Prob. 1.23PCh. 1 - The population data for a certain country are...Ch. 1 - Prob. 1.25PCh. 1 - Quenching is the process of immersing a hot metal...Ch. 1 - The useful life of a machine bearing depends on...Ch. 1 - 1.28 A certain electric circuit has a resistor and...Ch. 1 - 1.29 Water (of volume 425 ml) in a glass measuring...Ch. 1 - Consider the milk container of Example 1.4.2...Ch. 1 - Consider the milk container of Example 1.4.2...
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