Elements of mechanical engineering (notes)

E ıe m e n ts o f M e c h a n ic a ı
E n g in e e r in g
B y
M d M a n ir u z z a m a n
3 ' 4
Y e a r S tu d e n t
C o ııe ge o f T e x tile E n g in e e r in g
A n d T e c h n o lo g y,
D h a k a
B r o th e r s P u b ıic a tio n
2 2 1 ,
ıs ıa m ia M a r k e t
Ħilk h e t D h a k a 1 2 0 5

c o n te n ts
C h a p te r 1
T H E R M O D Y N A M ıc p R O C E SS E S O F p E R F E C T
G A S E S
C h ? p te r 2
E N G ıN E S
C h a p te r 3
B O IL E R
C h a p te r 4
( P u M p
C h a p te r 5
B E R N o U L L ı'
S E Q U A T IO N A N D ıT S
A p P L ıC A T ıO N S
C h a p te r 6
p R W ıO U S Y E A R q U E ST ıO N S

2
S o V a
PV a T P V «T
W h e n e C is a c o n s ta ru a n d it is k n o w n a s ge n e ra l g a s c o n s ta n t
T ĥ e riostg e n e ra l fo rm is
P ıV j P ıV ıË
W h r e th e s u ffix e s 1 2 R e fe r to d iffe re n t s e ts o f c o n d itio n s
C lıa r a c te r is tic s e q u a tio n o f G a s
It is th e m o d ifie d fo rm o f g s e q u a tio n If th e o lu m e in the g e e ra ı
g a s e q u a tio n ţs ta k e n a s th t o f IK g o f g a s (kn o n a s s p o ım e ) a n d
d e m o t d b y V s th e n th e c o s ta t C i th e g e n e a l g s e q tio n is
e p s e n te d b y n o th e r c o n s t n t R (is the c h a a c t is tic s g a s
e q a tio n ) T h e n th e g e n e a l g a s e q tio n is ń tte n a s P V R T
W be re R is k o a s g a s s ta t o r s i p ly g a s c o s ta t F o r a y
rıJa s s k g o f a g a s c h a ra c te is tic s
m P V s n R T
O P V R T [M V s v ]
一
K g
u n it o f R ・ K g m /k g k
N m
F o r S I u n it R
K g k K g k
P r o b le m l A g a s o c c u p ie s a o lu m e o f 0 10 5 m a t a te m p e r a tu r e
o f 2 0 c a n d a p e s s u r e o f iS k y c m
ı
fın d th e f n a ıte m p e r a tu e o f
th e g a s ir it is c o m p r e s s e d to a p r e s s u r e o f 7 S k g/c m
2
a n d
o c c u p ie s th e v a lu e o f 0 0 4 m
H e re P l 5 kg /c m l 5 × 104 k g lrn
2
V 0 10 5 m
3
T 2 0 C (27 3 + 2 0 )K 29 3 k
Th e rm o d yn o m lc P r o c e s s e s o f P e r le c f
P ï 7 5 k g /c m 7 5 × IU kg/m
y 2V 2 0 0 4 m
3
T t ?
￡L Y L
P z
V z
W e k n o w
T l T ,
= 12
P z
V z T Ï
P V
7 5 x l0 × 0 0 × 29 3
1 5 × ]0 0 10 5
5 5 8 0 95 K 2 85 0 9 C
A n s 2 8 5 0 9 C
S p e c ific h e a t o f a g a s
T łi s pe c ific h e a t o f s u b s t n c e m a y be b o a d ly ? fın e d a s th e
o t f he a t e q u i e To ra is e th e te m p e r a tu r e o f its u n it m a s s
th o u g h o n e d e g e e A ll th e liq id a n d s o lid s h a v e o n e s p e c iħ h e a t
o n ly B u t a g a o n h a n y n u m be r o f s p e c ific h e a t d e p e n d in g
u p o th o n d itio s d w h i h it i h te d T h e fo llo i g l o
typ e s o f s pe c ific he a ts o f a g s r im p o r ta t f o m th s u b je c t p o i t
o f v ie w
1 S p e c ific he a t a t c o s ta n t v o lu m e
2 S p c ific he a t a t c o s t n t te m p e t r
S p e c ifıc h e a t a t c o n s ta p t v o lu m e
It is the a m o u n t o l h e a t re q i d to ise the te m pe a t re o f a u n it
m a s s o f ga s th o u gh o n e d e g re e h e it is h e a te d a t c o s ta n t o lu m e
It is ge e ra lıy d o te d b y C v
L c L m m a s s o f the ga s
T In itia l te m p e ra tu re o f th e g a s
T 2 fi a l te m p a tu e o f th e g a s
J
T o ta l h e a t s u pp lie d to th e ga s a t c o n s ta n t v o lu m e
Q 12 m a ș s (s p e c ific he a t " " n s ta n t v o lw (ū s c Į" " p
m C v (T 2 T l)
Eıe m e n ts o f M e c h a n ıc o lE n g ın e e rın g
ĝ Ą ĝ母树耄ã §T

6 E le n n n fs o f o n k o l E m e e rlh g
T o ta ıw o rk d o n e fo r n o n n o w p ro c e s s fro m s ta te 1 to s ta te 2
į f v 2 2 2
W łz d w P d v p [v ] P (v ,
V )
E x a m p ıe T h e r m o d y n a m ic s p r o c e s s
(i) C o n s ta n t v o lu m e p r o c e s s
(ii) C o n s ta n t p r e s s u re p ro c e s s
(iii)Is o the r m a l p ro c e s s /c o n s ta n t te m p e ra tu re pro c e s s
(v ) P o lyrr o p h ic pro c e s s
c o n s ta n t v o ıu m e p r o c e s s
- w
o r k ? n e W P cv z
V ) O
d u m a (了2 T
d q d u + d w
q a u
m c o n s ta n t p r e s s u r e p r o c e s s
￡zv
T l n
> V
T 2
Ť 平 C o n s ta n t m R
W P (V z V t) m R (T 2 T ł)
> p V P V P V (T c o n s ta n t) C o n s ta n L
W o r k do n e b y the ga s d w Pd v
2 2
Įaw
Įp d "

A ť f ]3
￡
T
ŁĮ L
o 7 × ıOP ×
0 2 10
225 K = 225- 73
9 5 2 C A n s
2 M a s s f th e ga s
Lt t m M s f th g
W c k th t P u R T
R T 2 8 7 × 35 0
. 9 7 kg An s .
3 C h a n g e in i ı a ıc r w
W c kn o th a t c ha ge in in u a l n e rg y
d U LI m c u (T T )
0 59 7 0 7 12 (12 25 3 50 )
525 k ï A n s
4 C h a n ge in e n th a lp y
W e kn o ïıa t c h a n ge in e n th a ıp y
d H H H m c fT T )
0 5 9 7 × ı0 0 5 (12 2 5 35 0 ) 525 l【J A n s
P
E le m e n ts o f M e c h a n ic a l E n g in e e r ın
ł ł t
ţ
1
į J t L T i
v i !
th e m o d
Yn a m lc P ro c e s s e s o f P e r fe c t G a s e s
0 7 12 kJ/k g K
R 2 8 7 J/k g K
1 T e m p e r a tu r e a l th e e n d o f p r c e s s
L t T T e m p e ra tu e a l th e d f th p c s
Ł Ł
W e k n th t
T T

6 E le m e n ts o f M e c h o n lc o l E n g in e e rin g
E x a m p ıc 4 A q u a n tity o r g a s iıa s a v o lu m e o f 0 14 m
3
p r e s s u r e
L 5 b a r a n d a te m p e r a tu r e 10 0 C ir th c ga s is c o n ıp r e s s e d a t a
c o n s ta n t p r e s s u r e u n ï iıits v o lu m e b e c o m e s 0 ] 12 m d e te r m in e
] Th e te m p e r a tu r e a t th c e n d o f c o m p r e s s io n ; 2 w o r k d o n e o n
c o m p æ s s in g th e ga s ; 3 D e c r e a s e in tc r n a ıe n e r g y ; a n d 4 H e a t
g iv e n o u t b y th ga s
A S s u m e c l 0 0 5 k 】/kg K
1 ľ V §
a n d R 2 85 J/kg K l f łn į ıi n i }
T he c o m p re s s io n o f g a s a l c o n s ta n t p e s s u re is s h o w n in F ig 3 7
1 T e m p e r a tu r e a t th e e n d o f c o m p e s s io n
L e t T z T e m p e ra tu re a t th e e n d o f c o m p re s s io n
鱼主W e kn o th ı
T T « 3 :
mT z
O ] ] × 3 7 3
O ]4
ţ ł
2 9 8 4 K
2 9 8 4 27 3
T
r )
f
lŲ v t
2 5 4 C A s
2 W o r k d o n c is c o n 】p r e s s in g th e g a s
W c k n o w th t w o r k d o n e in c o m p re s i g th e ga s
W , 2 P (U u t)
0 15 × 10 (0 14 0 1 12 ) 4 2M U
#
田
4 2 kJ A ıs
3 D e c r e a s e in iııte m a l e n e r g y Ţ
F ia t o f a ll Je t u s lin d the m a s s o i g a s ([n a d m iu J í m p re s s i n
W e k n o w tıia t ll bı m 尺丁
rh e rm o d y n o m lc p ro Èe s s e s o f P e r fe c t G a s e s 1 7
R T
0 15 × ı0 × O ]4
28 × 3 7 3
W e kn o w tha i de c re a s e in in t r n a ıe n e rgy
d u U U z m c (T T )
0 19 7 × 0 7 12 (3 12 (37 3 29 8 4 )
10 4 6 k ï A n s
4 H a t g iv e n o u t b y th e g a s
W k n o th a t he a t g i c n o u t b y th e ga s
Q m c (T T )
0 19 7 × I 0 0 5 (3 7 3 2 9 8 4 )
14 7 7 k J A
E x m p ıe 5 A q a tity o r a ir h a s a o ıu m e o f 0 4 m
3
a t a
p s u l 5 b r a n d t m p e r a tu r e o f 8 0 lt ts e x p a n d e d in a
c y ıin d c r a l c n t t t m p r tu r e to a p r e s ￠u r e o f 1 b a r
D tc in e th e m u t o f o r k d n c b y th e a ir d u r in g e x p a n s io n
S o l tio n
G i e : U 0 4 m
3
P 5 b 0 5 l 10P N /m
- 0 °
P
Z
1 ba r 0 I × [đi
Ń/m
! ıĤ « j t w % į
F irs t o f a ll Ie t u s fin d th e o lu m e o f áir a t the c n d o f cxpatiön (ie
u ) W e kn o w tha t 9 J

18
m i L
Ele m e n fs o f M e c h a n ic a lE n g in e e rin g
andexpnsion ra tio u / u 2 / o 4 5
W e k n o w th a t w o r k d o n e b y th e a i đu r in g e x p a n s io n
W 2 3 p u lo g r t
2 3 × 0 5 × 10 × 0 4 lo g 5J
0 4 6 × 10
6
× 0 6 9 9
3 2 ı5 4 0 J { u b m /JUıI
3 2 1 54 k ] A n s
E x a m p ı 6 0 1 m o f ir a t a p e s s u r e o f ı5 b a r is p a d e d
is o th e r m a lly to 0 5 m C a lc l te th e fi ıp r e s s u e o f th e g a s a n d
h e a t s u p p ıie d d u i g th e p r o c s s
Aaļ ł } ￡ ł lţ
S o ıu tio n
Ş I d b ı W
G i D 0 l : p ] l 5 3
b a r 0 15 × 10 N /m ; ł Q ?
U 0 5 ī/ 1 4 f ļ
F i l p e s s u r e o f th e g a s
+o Į ll p ł ř
L e t p z i l p e s s r o f th g a s b d l + l p
w k n o w th a t p u p u
:
:Ií
ï
0 0 3 × lo N ln ł
0 3 ba r A n s
p
H e a t s u p p lie d d u r in g th e p r o c e s s
W e k ņo w tha t
:
e x p a n s io n Į a tio lļ ín : Į l Z・
W o r k d o n e d u r in g p ro c ee s s
W 2 3 p lu ıo g r 2 3 × 0 15 × 10 6 × O l Io g 51
:
0 0 34 5 × 10 x 0 699
Ų
ï h e r m o d yn o m ìc P r o c e s s e s o f P e r ıe c l G o s e s 19
24 I I5 J 24 I 15 U
W e kn o w tha t i is o th e rm l p ro c e s s he a t s u p p lie d (Q ) is e q u a l
1o the o k d o n e d u in g th e p o c e s s
Q W 2 4 I 15 k ï A n s
E x a m p ıe 7 0 n e lite r o f h y d o g e n a t W C is s u d d e n ly c o m p r e s s e d
to o n e h a ıf f its o ıu m e n n d th e c h a n g e in te m p e r a tu r e ď th e
g a s ir th e r a ti f t o s p c c ilic h a ts fo r h y d o g e n is 1A
S o lu tio n
G i n u 1 ıite r
T l O C 0 + 2 7 3 2 73 K
U U /2 2 0 5 lite r 了 I 4
L t T F i l t p t f lh ga s
w k th .
Kt}
ĺ ) (0 5 ) o 7 5 8
T T / 0 7 5 8 2 7 3 / 0 7 5 8 36 0 16 K
360 16 2 7 3 87 16 C A n
E x a p l 8 : T h e in itia l o l m e o f 0 18 k g o f a c e r ta in p a s w a s
0 15 m a t a te p e r a tu r e f 15 C a n d a p r e s s u r e o f 1 b r A fte r
a d ia b a lic c o m p e s s io to 0 0 5 6 th e p r e s s u r e w a s fo u d to
4 b a r F i d
l G a s c s ta n t; 2 M o le c la m s s o f th e g a s 3 R a tio o f , pe c °
h ts ; 4 T o s p e c ific h e a ts o n e a t a c o n s ta n t pre ss u re a n d th o th
t a c o n s ta n t v o ıu m d 5 C ha n g o f ¡n te m a l e n e r gy
s ı tio
G i e ：田 0 18 k g ；u 0 15 加 3
T 15 C 15 + 27 3 2 8 8 K

n ic o lE n g in e e rın g
W e k n o th a t w o rk d o n e b y th e n ir d u r in g e x p a n s io n
W 2 3 p u ıo g r
2 3 × 0 5 × 10 6
× 0 4 ıo g 5J
0 4 6 × l0 x 0 699
3 2 1 5 4 0 J
3 2 t 54 k Į A n s
E x a m p le 6 0 ı m o r a ir a t a p r e s s u r e o f ı5 b a r is e x p a n d e d
is o th e r m a ıly ro 0 5 m C a ıc u ıa te th e fin a l p r e s s u r e o f th e g a s a n d
h e a t s u p p lie d d u r in g ih e p r o c e s s
S o l tio n
G i e n u 0 1 m : p I I 5
b a r 0 ı5 × ]0 N /m P
u z 0 5
F in a ıp r e s s u r e o f th e g a s
L e t p a F in a l p r e s s u re o f th e g s
W e k n o w th a t p u pz u
P
0 15 × 10 x 0 1
0 2 0 5
0 0 3 × lo N /m
0 3 b a r A n s
H e a t s u p p lie d d u r in g th e p r o c e s s
W e k n o w th a t e x p a n s io n aio
r u /u 0 5/0 I 5
W o r k d o n e d u rin g th e pr o c e s s
W , 2 3 p lu lu g r 2 3 × 0 15 x 10 6 × 0 I ıo g 5J
0 0 34 5 × 10 x 0 6 9 9
lh e r m o d y n o m lc P ro c e s s e s o f P e r fe c t G o l e s
24 1 15 1 24 ı15 k ï
19
W c kn o th a t in a n is o the rm a l p o c e s s he a t s u p p lie d (Q ) is e q u a l
to the w o rk d o n e d u rin g th e p ro c e s s
Q W 2 4 ] 15 kJ A n s
E x a m p ıe 7 : O n e ıite r o f h y d o g n a t 0 C ıs s u d d e n ıy c o m p r e s s e d
to o n e h a ıf o f its v o lu m e fin d th e c h a n ge in te m p e r a tu r e th e
g a s if th e r a tio o f tw o s p e c if c h e a ts fo r h y d r o g e n is I 4
s o ıu tio n
G iv e n u l lite r
T l O C O + 2 73 2 7 3 K
U U /2 1/2 0 5 ıite r y ł4
L e t T F in a l te m p e ra tu r e o f the g a s
w . k " h
ĹT
(°
i
5
) (o 5 )
°
2 0 7 5 8
T T / 0 7 5 8 2 7 3 / 0 7 5 8 36 0 16 K
6 0. 6- 7 3 - 7. 6° An s .
E x a m p ıc 8 T h e in itia l o ıu m e o f 0 1 8 k g o f a c e r ta in p a s a s
0 15 m a t a te m p e r a tu r e o f 15 C a n d a p r e s s u r e o f 1 b a r A fte r
a d ia b a tic c o m p r e s s io n t 0 0 5 6 n ı th e p r e s s u r e w a s ro u n d to tie
4 b a r F in d
1 G a s c o n s ta n t; 2 M o le c l m a s s o f the ga s ; 3 R a tio o f spccifich e a ts ; 4 T w o s p e c ific he a ls o n e a t a c o n s ta n t pre s s u re a n d the o th e r
a l a c o n s ta n t v o ıu m e ; a n d 5 C h a n g e o f internal e n e r g y
S o ıu tio n Ţ

1 8 E ıe m e n ts o f M e c h a ı
a n d e x p s io n r tio r o / u 2 2 / 0 4 5

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