40 x 41f] cm square duct
P717 Air at 20°C and 1 atm enters a 40- Boundary layers
cm—square duct as in Fig. P17. Using the
“displacement thickness“ concept of Fig. 7.4.
estimate (a) the mean velocity and (b) the
mean pressure in the core of the ﬂow at the
5.15The wall shear stress w in a boundary layer is assumed to be a function of stream velocity
U, boundary layer thickness , local turbulence velocity u, density , and local pressure gradient
dp/dx. Using (, U, ) as repeating variables, rewrite this relat
P4.2 Flow through the converging nozzle
in Fig. P42 can be approximated by the
one-dimensional velocity distribution
\
2 x
Hal/g[l+—
U 2 0 11‘ 2 0
X
(a) Find a general expression for the ﬂuid
acceleration in the nozzle. (1) For the
specific case V0 = 10
P4.43 For the draining liquid fihn of Fig.
P436. what are the appropriate boinldary
conditions (a) at the bottom is : 0 and (b) at
the s1u‘face_1-'= if?
Fig. P436
Solution: The physically realistic conditions at the upper and lower surfaces are:
(a) at
This is a mistake in the solutions. Kerosene has a viscosity of 0.00192. A viscosity of 0.0192 is closer to
that of ethylene glycol, which has a viscosity of 0.0214.
2.149 The waterwheel in Fig. P2149 lifts
water with l-ft-dianleter half-cylinder
blades. The wheel rotates at 10 r/nn'n. What
is the water surface angle 6* at pt. A‘?
Solution: Convert Q = 10 Ifnlin =
radfs. Use an average radius R : 6.
Then
ft. —+1 1 f
2.86 The quarter circle gate BC in
Fig. P2.86 is hinged at C. Find the
horizontal force P required to hold the gate
stationary. The width E) into the paper
is 3 m. Neglect the weight of the gate.
Solution: The horizontal component of Fig_ p236
water for
P2.4 Pressure gages. such as the Bourdon gage
in Fig. P24= are calibrated with a deadweight piston.
Ifthe Bourdon gage is designed to rotate the pointer q
,_ cm
diameter
10 degrees for ever 2 psig of internal pressure, how
many degrees does the pointer