Wilk the veloci.fy 1-Ylan9le we comaide 'that
V = v, sly, 3o = V, co. s 6o = (15 /n)(s/r7 70 .)=7-5- L
= <999 kg )(7.s 127) 27(2 /77)(1 m)
A/so, will, /he trio qk we see 'ha/
Then, with El
= 8 ft/s
Two jets of liquid, one with
specific gravity 1.0 and the other with specific gravity 1.3, collide and form one homogeneous jet as shown in Fig. P5.11R.
Determine the speed, V, and the direction, 0, of the combined
jet. Gravity is negligibl
5. 6 R
A horizontal circular jet of air
strikes a stationary flat plate as indicated in Fig. P5.6R. The jet
velocity is 40 m/s and the jet diameter is 30 mm. If the air
velocity magnitude remains constant as the air flows over the
plate surface in the
The single stage, axialflow turbomachine shown in Fig. P5.15R involves water flow
at a volumetric flowrate of 11 m 3 /s. The rotor revolves at 600 11 m'is
rpm. The inner and outer radii of the annular flow path through
the stage are
Thus, since 4.-47.R2 4(1) becomes
rRz 4 VP"
zze (4-R2).14/- '
We can cleierinthe 214 in /epos of Al Zy using /he conilnaly eFai ion;
e cm 0, or since e consivq"
/.14 d A -.4 Ar il-f](2.7rreir)
2 7r0. R 2 1(X X 2 ) the
ni = 1000 Ibm/s
Water flows through a right angle valve at the rate of 1000 lbm/s as is shown in Fig. P5.5R.
The pressure just upstream of the valve is 90 psi and the pressure drop across the valve is 50 psi. The inside diameters of the
valve inlet a
A nozzle is attached to an 80mm inside-diameter flexible hose. The nozzle area is 500 nun'- .
If the delivery pressure of water at the nozzle inlet is 700 kPa,
could you hold the hose and nozzle stationary? Explain.
An axisymmetric device is used
to partially "plug the end of the round pipe shown in Fig.
P5.7R. The air leaves in a radial direction with a speed of 50
ft/s as indicated. Gravity and viscous forces are negligible. Determine the (a) flowrate through
A horizontal air jet having a
velocity of 50 m/s and a diameter of 20 mm strikes the inside
surface of a hollow hemisphere as indicated in Fig. P5.9R. How
large is the horizontal anchoring force needed to hold the hemisphere in place? The magnitude of
Asphalt at 120 F, considered to be
a Newtonian fluid with a viscosity 80,000 times that of water
and a specific gravity of 1.09, flows through a pipe of diameter
2.0 in. If the pressure gradient is 1.6 psi/ft determine the
flowrate assuming the pipe
Water flows steadily through
a 2-in.-inside-diameter pipe at the rate of 200 gal/min. The 2in. pipe branches into two 1-in.-inside-diameter pipes. If the
average velocity in one of the 1-in. pipes is 30 ft/s, what is the
average velocity in the othe
Water at 0.1 m 3 /s and alcohol
(SG = 0.8) at 0.3 m 3 /s are mixed in a y-duct as shown in Fig.
P5.3R. What is the average density of the mixture of alcohol
Q = 0.1 m 3/s
Alcohol (SG = 0.8)
Q = 0.3 m 3/s
protection association code requires a minimum pressure of 65
psi at the outlet end of a 250-ft-long, 4-in.-diameter hose when
the flowrate is 500 gal/min. What is the minimum pressure
allowed at the pumper truck that supplies water to the ho
. ,Thilti i ii
The three tanks shown in Fig.
P8.16R are connected by pipes with friction factors of 0.03 for
each pipe. Determine the water velocity in each pipe. Neglect
t = 7
A fluid flows through a pipe of radius R with a Reynolds number of 100,000. At what location,
r/R, does the fluid velocity equal the average velocity? Repeat
if the Reynolds number is 1000.
For Re= 10 5, Ti -= (1 f) n , where n =7.1 (see Fig.
The pump shown in Fig. P5. I 8R
adds 20 kW of power to the flowing water. The only loss is that
which occurs across the filter at the inlet of the pump. Determine
the head loss for this filter.
0.05 m 3/s
The energy epalion for /his flow can
SY, R coniinued
*ie energy eguabO),
12 Pz 7'
2)1- la( foss)
As SUff esied
-3 I I
e(e-es2).-i_crs;, ,-(e, nxio
111 1+ 2 Id
(6- s:.f3) we
O. Seelig>, 5; 2.2
shaw-.: -0.0107 cfw_f l6
(minur fir mean love oppose!
( 0,0107 7c4.
r!t, )(21r- ;211
- 0.336 s. l6
(minus- sir, means- work
if OW L oil
.5 - 2 3 R
A lawn sprinkler is constructed from pipe with +-in. inside diameter as indicated in Fig.
P5.13R. Each arm is 6 in. in length. Water flows through the
sprinkler at the rate of 1.5 lb/s. A force of 3 lb positioned
halfway along one arm holds the spri
Water flows steadily from one
location to another in the inclined pipe shown in Fig. P5.17R.
At one section, the static pressure is 12 psi. At the other section,
the static pressure is 5 psi. Which way is the water flowing?
p = 5 psi
5, /9 R
Eleven equally spaced
turning vanes are used in the horizontal plane 90 bend as indicated in Fig. P5.19R. The depth of the rectangular crosssectional bend remains constant at 3 in. The velocity distributions upstream and downstream of the
A small water turbine is
designed as shown in Fig. P5.I6R. If the flowrate through the
turbine is 0.0030 slugs/s, and the rotor speed is 300 rpm, estimate the shaft torque and shaft power involved. Each nozzle
exit cross-sectional area is 3.5 x 10 -
Water flows vertically upward
in a circular cross-sectional pipe as shown in Fig. P5.12R. At
section (1), the velocity profile over the cross-sectional area is
uniform. At section (2), the velocity profile is
where V = local velocity vect
S OR tLine:ir monwf it If al
Determine the magnitude of
the horizontal component of the anchoring force required to
hold in place the 10-foot-wide sluice gate shown in Fig. P5. 10R.
Compare this result with the size of the horizontal component
5. 9R conlinved
n1,), 7- )
a a 05
2 ( -zoo -*Pa o -APR) (Soo p.m')
0. off5,2 .7
0000 .-, 2
F' . 707 N
-terms of a
.: 707 N
V= 50 ft /s
Air (assumed incompressible)
flows steadily into the square inlet of an air scoop with the
nonuniform velocity profile indicated in Fig. P5.2R. The air
exits as a uniform flow through a round pipe I ft in diameter.
(a) Determine the avera
5, 7R conlinved
For FA r+
(C. ) VW- de-442:f ni .1
point (1), by oi.vkiinci tile_
(2) . Thus, since V2. 0 1
iivt 1709 e. ? ve55 Lae
s_Lla \X I tb,st
S 5 R con f in uedl
, in the y-direcilon
arl e(111 74- 4V)./
4 Arz el urtmri,i).(- t)Az = 70,4
(-VI )e(-V1 )/91 +0= -1)1 4 -e-F;?),
or Fhy % /2/ 4
*e442 71,4 #th
(2) 2 V = (ff2:7 ) (r.92q) = /9.7
Fr = 9o-t (
The flow in an open channel has
a velocity distribution
V = U(y1h) 111 ft/s
where 11 = free-surface velocity, y = perpendicular distance
from the channel bottom in feet, and h = depth of the channel
in feet. Determine the average velocity of the chan
Pump hea d, ft of wa ter
A pump transfers water from one
large reservoir to another as shown in Fig. P5.21Ra. The difference in elevation between the two reservoirs is 100 ft. The
friction head loss in the piping is given by K,V 2 12g, where V