Government Engineering College - Bhuj

COMPRESSIBLE FLUID FLOW• STUDENT NAME:- PARMAR UMANG R.• SUDENT ENROLLMENT NO.:-130150119076

FLUID MECHANICS

Example :- 1 An air vessel is flying at 215 m/s at a low altitude

where the velocity of sound is 325 m/s. At a certain point just outside the boundary layer of the wings, the velocity of air relative to the plane is 305 m/s Determine the pressure drop on the wing surface near this position. Assume frictionless adiabatic flow and take pressure of ambient air 102 KN/ and

2m .4.1

1

1

2

2

1

1

121

2

1

1

2

1

121

22

22

2

221

1

1

&,

112

2121

P

PPaSince

P

PPVV

VPVP

1

1

2

2

1

1

121

2

1

1

2

1

121

22

22

2

221

1

1

&,

112

2121

P

PPaSince

P

PPVV

VPVP

22

12

4.0

4.1

1

1

2

2

22

21

21

22

1

1

2

1

1

221

21

22

/7305410721.0721.0

721.0911.0911.0

911.0

325

215305

2

14.11

2

11

112

mKNPP

P

P

a

VV

P

P

P

PaVV

Where a = velocity of sound

Hence, pressure drop on the wing

......./46.28

54.731022 AnsmkN

Example :- 2 Find the velocity of a bullet fired in standard air if

mach angle is 30 degree. Take R=287J/Kg=1.4 and T=15degree C.

soln.:

KT

K

KKgJR

angleMachGive

288

4.1

/287

30,

smC

C

KRTC

/25.340

2882874.1

WE know that velocity of sound ‘C’ is

......../50.68030sin

25.340

25.34030sin

sin

AnssmV

V

V

V

CAlso

Example :- 3 A flying object is flying at a speed 1100 km/hour at sea level at a temperature of . Take K=1.4 and Find the Mach number at a point on this flying object. Soln.: Speed of object, V = 1100km/hour =1100*1100/60*60 = 305.55m/s

C20 ./287 KKgJR

.......89.011.343

55.305

/11.343

2932874.1

/287,4.1

29327320

AnsC

VMBut

smC

C

KRTC

KKgJRK

Ktetemperatur

We know that, sound velocity C is

Example :- 4 Find the speed of sound in air at an altitude of 5000 m.

At 5000 m, T = 255.7 K.

CkJ

kg KK

ms

kJkg

m

s

14 0 287 25571000

3205

2

2

. ( . )( . )

.

Notice that the temperature used for the speed of sound is the static (normal) temperature.

Example :- 5 An aircraft flies in air at 5000 m with a velocity of 250

m/s. At 5000 m, air has a temperature of 255.7 K and a pressure of 54.05 kPa. Find To and Po.2

2

2

2

250255.7

2 2(1.005 ) 1000

(255.7 31.1)

286.8

oP

kJmV kgs

T T KkJ mCkg K s

K

K

kPa

K

K

T

TPP

kk

77.80

7.255

8.28605.54

)14.1(4.1

)1(

Thank You…