You are filling a cylindrical drum (D = 22.5 in., H = 33.5 in.) with water flowing from a garden faucet at a rate of 10 GPM. How long will you have to wait to fill the drum? Express
you answer in minutes.
Answers
Using
n
1
A
1
¯
v
1
=
n
2
A
2
¯
v
1
,
assigning the subscript 1 to the aorta and 2 to the capillaries, and solving for
n
2
(the number of capillaries) gives
n
2
=
n
1
A
1
¯
v
1
A
2
¯
v
2
.
Converting all quantities to units of meters and seconds and substituting into the equation above gives
n
2
=
(
1
)
(
π
)
(
10
×
10
−
3
m
)
2
(
0.27
m/s
)
(
π
)
(
4.0
×
10
−
6
m
)
2
(
0.33
×
10
−
3
m/s
)
=
5.0
×
10
9
capillaries
.
Discussion
Note that the speed of flow in the capillaries is considerably reduced relative to the speed in the aorta due to the significant increase in the total cross-sectional area at the capillaries. This low speed is to allow sufficient time for effective exchange to occur although it is equally important for the flow not to become stationary in order to avoid the possibility of clotting. Does this large number of capillaries in the body seem reasonable? In active muscle, one finds about 200 capillaries per
mm
3
,
or about
200
×
10
6
per 1 kg of muscle. For 20 kg of muscle, this amounts to about
4
×
10
9
capillaries.
Hope it helps ❤️⚡
angle of incidence is {{60}^{0}}600 and angle of refraction is{{30}^{0}}300, then refractive index of medium , You are filling a cylindrical drum (D = 22.5 in., H = 33.5 in.) with water flowing from a garden faucet at a rate of 10 GPM. How long will you have to wait to fill the drum? Express
you answer in minutes.