Heart Attack!
A human heart discharges 7 5 ml of blood during each beat against a pressure of 0 . 1 mm of mercury. Calculate the power of the heart assuming the following facts:
1.)Pulse Frequency: 8 0 beats per minute
2.)Density Of Mercury: 1 3 6 0 0 kg/m 3
3.)Acceleration due to gravity: 9 . 8 m/s 2
Details and Assumptions :
Use the exact value of atmospheric pressure. Multiply your answer by 1 0 0 0 0 0 . Give your answer in Watts.
The answer is 133.2.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
3 solutions
Its interesting that the Ideal Gas Laws is applied here . 'Cause Gas Laws are applicable for Ideal Fluids- which corresponds to Boyle's Law . But blood is not an ideal fluid .
And you know gelatin, blood are Non- Newtonian Fluid !
LEARN LATEX you TOPPER
Log in to reply
Thanks for pointing out.. It is indeed 10000.. @Vaibhav Prasad @Kalash Verma .. Moral of The story: FIITJEE ki book mei answer galat hai :p
Log in to reply
@Kalash Verma @Harsh Shrivastava @Hrishik Mukherjee
all of you try this
Log in to reply
@Vaibhav Prasad – Answer mei kya likhna hai.. All 3 or just 1. Waise that equation is a perfect square only for 3 numbers AFAIK.
Log in to reply
@Hrishik Mukherjee – can you please tell me which THREE NUMBERS ????
Log in to reply
@Vaibhav Prasad – − 1 , 0 , 3
Log in to reply
@Harsh Shrivastava – Yo i edited the question
Hey! have you edited the question? My answer is still wrong
Log in to reply
@A Former Brilliant Member – I have tried 13.328 it was declared wrong. Then I tried adding the atmosphere it was still wrong.How can i get my answer right?
Log in to reply
@A Former Brilliant Member – ans 13.328 nhi 133.2hai
Log in to reply
@Vaibhav Prasad – Well in the question 100000 was given 10000 first when I solved it therefore in that time right answer was 13.328
Check your calculation cause your answer is coming 0.1332.but by calculating your expression answer is coming 0.0013328 in line 13. Therefore answer is comimg 13.328 after multiplying it by 10000.@vaibhav prasad pls recheck
Log in to reply
oh yes @Kalash Verma you are very right he should say 'multiply by 1 0 0 0 0 0 '
@Kalash Verma , even @Vaibhav Prasad arrived at the same result. Vaibhav, I shall learn it later. @Harsh Shrivastava Tu bhi karke dekh be :p
Log in to reply
Bhai hrishik tera answer sahi hai bas tujhe 'multiply by 10000' ke jagah par 'multiply by 100000' likhna chahiye tha :)
Nice solution!!
If we assume that the density of the blood must be constant then we know that c = A v , where A is the cross-section of a vessel and v is the velocity of the fluid (blood) in the vessel, must be also constant. We may therefore write
P = F v = Δ p c ,
where P is the power and F is the force the heart must excert to pump the fluid agains the pressure Δ p = 0 . 1 mmHg ≈ 1 3 . 3 Pa . The volume may be written
A f v = f c = 7 5 ml ,
where f is the pulse frequency. Therefore the power is
1 0 5 P ≈ 1 3 . 3 ⋅ 7 . 5 ⋅ 6 8 = 1 3 3 W .
Pressure * Volume in kg-m...Pressure * Volume * g in N-m or J.....
Pressure * Volume * g per time in J/s=Watt...........
{
1
3
6
0
0
∗
(
0
.
1
∗
1
0
−
3
)
}
∗
(
7
5
∗
1
0
−
6
)
∗
9
.
8
∗
(
6
0
8
0
)
=
1
3
3
.
2
8
∗
1
0
−
5
a
n
s
w
e
r
=
1
3
3
.
2
8
Pulse Frequency = 80 beats/minute = 8/6 beats/minute Blood discharged per beat = 75 ml Blood discharged per second = 75*4/3 = 100 ml/second
100 ml/second = 1/10 l/second = 10^-4 m^3/second
Atmospheric Pressure = 0.76 m * 13600 kg/m^3 * 9.8 m/s^2 = 101292.8 Pascals = 760 mm of Mercury
By unitary method, 1/10 mm of Mercury is equal to a pressure of 101292.8/7600 Pa
Therefore, power of the heart = 10^-4 * 101292.8/7600 = 0.001332 Watts Multiplying it by 100000 Answer = 133.2
Those who don't understand the power of the heart part, here is the explanation: Force/Area * Volume/Second = Force * displacement/second = POWER!!
PS. I regret not formatting my question and solution, but couldn't help. Suggestions and corrections are accepted 24x7 =D