CHEMENG 2018: PROCESS FLUID MECHANICS
TUTORIAL 3
MOMENTUM EQUATION, DIMENSION ANALYSIS & MODELLING (Due: 3 May 2023)
In your tutorial team, attempt all questions and submit your team’s best solutions to the following problems for assessment: 3.1, 3.2, 3.5 and 3.6
103.1 An oil (SG = 0.86) flows through the horizontal tee connection as shown in Fig. 3.1. The
of 0.5 m. Assume the flow is steady, uniform, incompressible and frictionless.
a. Find the flow rate of oil entering the line at section (2).
b. Calculate the pressures at sections (3) and (2).
c. Determine the components, magnitude and direction of the force exerted by the oil on the tee.
Ans: (a) 0.82 m3/s (b) 171 kPa; 208 kPa (c) Rx = –45.3 kN; Ry = 7.3 kN;–81o from y-axis y
dischargeflowrateQ atsection(3)is2.0m/sandeachpipesectionhasaninsidediameter 3
03.2 Calculate the magnitude and direction of the force required to hold the flow device in Fig. 3.2 stationary for the following situations. The fluid is water at 20oC, and the device and its content weighs approximately 600 kg. Assume that flow is steady, uniform and frictionless, and that pressures at all outlets are atmospheric.
a. Gravity is perpendicular to the x-y plane (of the paper); b. Gravity acts in the negative y-direction.
Ans: (a) 7.1 kN; – 14o from x-axis; (b) 8.1 kN; 31o from x-axis
3.3 An open tank of water is connected to a pipe having a uniform diameter of 75 mm, as shown in Fig. 3.3. Assuming the flow through the pipe is steady and frictionless, determine the following:
a. Flow rate of water flowing in the pipe in [m3/h].
b. The pressures at points A, B and C.
c. The magnitude and direction of the force acting on the pipe. State clearly any assumptions made in your calculations.
Ans: (a) 50 m3/h (b) pA = 24.5 kPa; pB = – 4.9 kPa (c) 108 N in horizontal flow direction Page 1 of 2
Q = 0.25 m3/s
v = 2.5 m/s 60o
Q = ? m3/s v = 1.5 m/s
Q = 0. 5 m3/s v = 2.0 m/s
p = 6.0 kPa
p1 = 200 kPa
Q = 0.75 m3/s v = 3.0 m/s
p = 8.0 kPa
浙大学霸代写 加微信 cstutorcs
C D = 0.1 m 0.5 m
3.4 The average diameter (d) of droplets formed when a liquid is sprayed from a nozzle depends on the fluid velocity (v) from the nozzle, the nozzle tip diameter (D), the liquid density () and viscosity (), the surface tension between the liquid and air (), and the gravitational acceleration (g). Apply the Buckingham dimensional analysis to find appropriate dimensionless groups for this process. Identify and name any familiar or standard dimensionless groups involved.
a. Use the method of dimensional analysis to determine the pertinent dimensionless groups for the process.
b. The model used is 1/5th in scale as compared to the prototype, and fluid density scale ratio is kept at 1.0. Can all similarity requirements be met with this model? What should the viscosity ratio be?
c. If a test from the model gives a critical velocity of 3.8 m/s, what would the predicted critical velocity in the prototype be (assuming all similarity requirements are satisfied)?
Ans. (a) A possible valid answer: Dvc =F d,s ,gD32 (b) m/p = 0.089 (c) 8.5 m/s D 2
*3.5 In hydraulic transport of solids by pipeline, when the fluid velocity exceeds a critical value, the solid particles will rise and be carried by the fluid along the pipe. A model pipeline system is to be used to study this critical velocity. From experience, the critical velocity (vc) is known to be a function of the pipe diameter (D), particle diameter (d), the fluid density (), the fluid viscosity (), the density of the solid particles (s), and the gravitational acceleration (g).
Ans.Apossiblevalidanswer: d =FDv, ,gD D v v2
a. By means of dimensional analysis, find the dimensionless groups pertinent to this problem.
b. How long should the model pipeline be?
c. If the average fluid velocities for the model and prototype are equal, at what temperature should the water be operated in the model pipeline? Assume that the gas is at atmospheric pressure.
Note: you need data of kinematic viscosity (or dynamic viscosity and density) of helium and of water as a function of temperature which can be found from fluid mechanics text-books or handbooks.
Ans.(a)Apossiblevalidanswer: p =FDu,L (b)0.8m(c)15.2oC
u2 D
*3.6 Helium gas at 20C is to be transported through a 80-m-long pipeline with an inside diameter (ID) of 0.6 m. To determine information about the flow in this pipeline, tests are to be conducted in a geometrically similar pipe with an ID of 6 mm and with water as the model fluid. The physical quantities are pressure drop (p), average fluid velocity (u), pipe inside diameter (D), pipe length (L), fluid density (), and fluid kinematic viscosity ().
Page 2 of 2
Tutorial 3
=>1,178+ Q2=2
=0 . 8 2 2 m
+ I 4 V , 2 + 2 , P g =4 3 + 2p(V,2-
1200x 103-2
=1200-29.17)
>P 3 =1 7 1 k P a
R x =P 1 A
Ry =P2An-P3A3+PVzQ2 – V
Rx 200x. 10
=39.27×103
=(39.27 +6.08) x10N
= >R x =4 5 . 3 5 k N
x6m/s =xr.5
Q2=0.82 mY/s=A
=Q3/A =2mYs/x
(7.26×103 –
=( 7 . 2 6 –
=7 . 3 8 k N
= >V 2 =a 2 / A
x10.53+860 x
14.63548) x10
+EPV3 + Z309
860(- 67.84)
08xx0.52-171×103 x x0.52 + 860x(4.19×0.
171)x103+ 8
ax Velocity – 178m/s
= >t a n t –
=2 0 0 k P a
=4 . 1 9 m / s
=200×10 =200×10
+ 1 9 2 1 =4 2
=(200+ 7.931) x
from y-axis -45.35KN,
+ PV22+ 1922
a+2 x860(62-
7930.877 Pa
1 =z 3 .P3 =200x10pa + x860kg/m3 (62 –
specific gravity
0 =086x1000kg/m =860ky/m
程序代写 CS代考 加微信: cstutorcs
number (Re) =
Froude number (Fr)=(rd)/(gD>
Reynolds number (Rep) = (pud)/M
Particle Stokes number (St) (psd2)/(18Mv)
=f(d,D,f,fs,g)
Re F(y,,1)
=exvolx9 Mx
scale ratio (2)=1
Time scale ratio
G =1 , 1 ) =1
io (V)=(((”
( T ) =( (
p ‘ , x 9 x4 xP unp
Reynolds law (Re)m =(Relp
I P r =1 P )
(volgrad) XA
Xv o l x m
) =(i)/0.58 =0.854
=3 . Oruls
( p =3 . 8 x = 6 8 9 x 4 5
( V ) p = 8 . 5 5 m / s =A n s
R e =A Ps t e n c e
=density =velocity =diameter
model length=100m … 0.8m dipeline
1.178×10-5
=1.178×10-7 m
(r t ** =(*)
Uwater =1.307 x10-m2/sec
Uwater =1.00
=7 =14.26°C a twhich
4×10″my/sec
x10 m2/sec