*P4.80 Oil, of density p and viscosity μ, drains steadily down the side of a vertical plate, as in Fig. P4.80. After a development region near the top of the plate, the oil film will become independent of z and of constant thickness 8. Assume that w= w(x) only and that the atmosphere offers no shear resistance to the surface of the film. (a) Solve the Navier-Stokes equation for w(x), and sketch its approximate shape. (b) Suppose that film thickness & and the slope of the velocity profile at the wall [w/dx] wall are measured with a laser-Doppler anemometer (✓ Chap. 6). Find an expression for oil viscosity μ as a function of (p, d, g, [ow/x] wall). Plate Oil film P4.80 Air 1
*P4.80 Oil, of density p and viscosity μ, drains steadily down the side of a vertical plate, as in Fig. P4.80. After a development region near the top of the plate, the oil film will become independent of z and of constant thickness 8. Assume that w= w(x) only and that the atmosphere offers no shear resistance to the surface of the film. (a) Solve the Navier-Stokes equation for w(x), and sketch its approximate shape. (b) Suppose that film thickness & and the slope of the velocity profile at the wall [w/dx] wall are measured with a laser-Doppler anemometer (✓ Chap. 6). Find an expression for oil viscosity μ as a function of (p, d, g, [ow/x] wall). Plate Oil film P4.80 Air 1
Question
solve part b only
![*P4.80
Oil, of density p and viscosity μ, drains steadily down the side of a vertical
plate, as in Fig. P4.80. After a development region near the top of the
plate, the oil film will become independent of z and of constant thickness 8.
Assume that w= w(x) only and that the atmosphere offers no shear
resistance to the surface of the film. (a) Solve the Navier-Stokes equation
for w(x), and sketch its approximate shape. (b) Suppose that film thickness &
and the slope of the velocity profile at the wall [w/dx] wall are measured
with a laser-Doppler anemometer (✓ Chap. 6). Find an expression for oil
viscosity μ as a function of (p, d, g, [ow/x] wall).
Plate
Oil film
P4.80
Air
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F216015d9-daff-4e98-b3d1-7f3f5202e820%2F4bede03e-c342-4058-915d-670827a9634a%2Fe89ltm8_processed.png&w=3840&q=75)
Transcribed Image Text:*P4.80
Oil, of density p and viscosity μ, drains steadily down the side of a vertical
plate, as in Fig. P4.80. After a development region near the top of the
plate, the oil film will become independent of z and of constant thickness 8.
Assume that w= w(x) only and that the atmosphere offers no shear
resistance to the surface of the film. (a) Solve the Navier-Stokes equation
for w(x), and sketch its approximate shape. (b) Suppose that film thickness &
and the slope of the velocity profile at the wall [w/dx] wall are measured
with a laser-Doppler anemometer (✓ Chap. 6). Find an expression for oil
viscosity μ as a function of (p, d, g, [ow/x] wall).
Plate
Oil film
P4.80
Air
1
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