Unit Conversion Examples

Unit Conversions

3

Unit Conversion Examples

1. A 6.00 slug mass experiences a 9300 N force. Find the acceleration, a (f = ma) in units of ft/sec2 and m/sec2

a

=

f m

=

9300N 6.00slug

1 slug - ft 1lbf - s2

1lbf 4.448N

a

=

f m

=

9300N 6.00slug

1 slug - ft 1 lbf - s2

1lbf 4.448N

=

346 ft s2

1m 3.2808ft

=

105

m s2

2. A m = 1 lbm of water yields about 1000 Btu of heat energy in condensing from steam to liquid. If the H2O also has a velocity of V1 = 950 ft/s as steam and V2 = 31 ft/s as liquid, find the total energy change for the condensation process, given by:

E = -1000 Btu + KE, where KE = m(V22 - V12 ) / 2

?

E

=

-1000Btu

+

(1lbm)

1 2

31

ft s

2

-

950

ft s

2

lbf - s 2 32.178ft - lbm

1Btu 778.16ft -

lbf

E

=

-1000Btu

+ (1lbm)

1 2

31

ft s

2

-

950

ft s

2

lbf - 32.178ft

s2 - lbm

1Btu 778.16ft -

lbf

E = -1000Btu + (-18Btu) =-1018Btu

E

=- 1018Btu

1055J 1 Btu

1010kJ0J

=

-1074kJ

3. The acceleration of gravity is 39 ft/s2 on Planet Zordar. Find the force of attraction (what we call weight, w = mg) of the gravitational field on a 25 lbm object in units of:

w

=

mg

=

(25lbm )

39

ft s2

lbf - 32.178ft

s2 - lbm

w

=

mg

=

(25lbm

)

39

ft s2

lbf - s 2 32.178ft - lbm

=

30.3lbf

4.448N lbf

=135N

Unit Conversions

4

4. The speed of sound in an ideal gas at temperature T is given by: c = (kRT)?

For air, k = 1.40 (dimensionless) and R = 53.3 ft-lbf/lbm-?R. Find the speed of sound at

T = 70?F = 530?R in units of ft/sec and mi/hr

( ) c

=

(kRT )0.5

=

(1.4) 53.3

ft - lbf lbm -o R

530o R

32.178ft - lbm lbf - s2

0.5

= 1130

ft s

c =1130 ft s

1mi 5280ft

60s 1min

60min 1hr

c =1130 ft s

1mi 5280ft

60s 1min

60min 1hr

=

769

mi hr

5. The units for exhaust emissions from internal combustion engines are frequently given in g/(hphr). Convert the following to the equivalent in the SI system, kg/(kW-day)

0.0376 g hp - hr

=

0.0376

hp

g -

hr

1010k0gg

1hp .746kW

24hr 1day

0.0376

g hp - hr

= 0.0376 g hp - hr

1kg 1000g

1hp .746kW

24hr 1day

=

1.21x10

- 3

kg kW - day

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