A block of mass M slides on a thin film of oil. The film thickness is h and the area of the block is A . When released, mass m exerts tension on the cord, causing the block to accelerate. Neglect friction in the pulley and air resistance. Develop an algebraic expression for the viscous force that acts on the block when it moves at speed V . Derive a differential equation for the block speed as a function of time. Obtain an expression for the block speed as a function of time. The mass M = 5 kg, m = 1 kg, A = 25 cm 2 , and h = 0 . 5 mm. If it takes 1 s for the speed to reach 1 m/s, find the oil viscosity μ . Plot the curve for V ( t ).
A block of mass M slides on a thin film of oil. The film thickness is h and the area of the block is A . When released, mass m exerts tension on the cord, causing the block to accelerate. Neglect friction in the pulley and air resistance. Develop an algebraic expression for the viscous force that acts on the block when it moves at speed V . Derive a differential equation for the block speed as a function of time. Obtain an expression for the block speed as a function of time. The mass M = 5 kg, m = 1 kg, A = 25 cm 2 , and h = 0 . 5 mm. If it takes 1 s for the speed to reach 1 m/s, find the oil viscosity μ . Plot the curve for V ( t ).
A block of mass M slides on a thin film of oil. The film thickness is h and the area of the block is A. When released, mass m exerts tension on the cord, causing the block to accelerate. Neglect friction in the pulley and air resistance. Develop an algebraic expression for the viscous force that acts on the block when it moves at speed V. Derive a differential equation for the block speed as a function of time. Obtain an expression for the block speed as a function of time. The mass M = 5 kg, m = 1 kg, A = 25 cm2, and h = 0.5 mm. If it takes 1 s for the speed to reach 1 m/s, find the oil viscosity μ. Plot the curve for V(t).
Block
2) A block of mass M slides on a thin film of
oil. The film thickness is h and the area of
Cord
the block A. When released, mass m exerts
tension on the cord, causing the block to
accelerate. Neglect friction in the pulley and
air resistance. Develop an algebraic
expression for the viscous force that acts on
the block when it moves at speed V. Derive a
differential equation for the block speed as a
function of time. Obtain an expression for the
block speed as function of time. The mass
M=5kg, m=lkg, A=25 cm?, and h-0.5 mm.
If it takes 1 second for the speed to reach 1
m/s, find oil viscosity u.
Oil film
(viscosity, u)
Mass
Sparky is on the university speed ice skating team. When crossing the finish line
Sparky wants to show off and come across the finish line on one skate with a velocity of 35
ft/sec (V). Sparky weighs 150 lbf. Sparky’s weight is supported by a thin liquid film of water
melted by the pressure of the skate blade. If the blade is 13 inches long and 0.125 inches wide
estimate Sparky’s deceleration resulting from viscous shear in a water film of thickness of
0.0000575 inches (h). Neglect all end effects. Evaluate all properties at 32°F. Suggest
creating a simple schematic of the problem using V, h, and the viscous shear stress (not
required).
Problem 2:
The capillary rise of a fluid along the walls of the tube causes the fluid to rise a distance h. This effect
depends upon the diameter d of the tube, the surface tension o, the density p of the fluid, and the
gravitational acceleration g. Show how to obtain the two Pi terms h/d and o/pd2g, where q = h and s
(meaning h and s are the non-repeating parameters). If an experiment is performed using water at a
temperature of 50°C, and the surface tension is s = 0.08 N/m, the following data is obtained of the
height h versus the diameter d of the tube. Use the data and plot the relationship between the two Pi
terms. Use the M-L-T System.
d
h (mm) d (mm)
60.12
30.06
20.04
14.84
12.02
10.02
0.5
NH
35555
1
1.5
2
2.5
Chapter 2 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
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