The heart of man pumps 4litres of blood per minute at a pressure of 130mm of mercuryIf density of mercury is 13.6g/cm3.Find the power of heart

0.02w

0.2w

3.2w

1.2w

Amit Tapas, 13 years ago

Grade:10

6 Answers

Shivam Bhagat

22 Points

13 years ago

power=work /time=f*d/t=f*v(v=velocity) Assume the area to be 1 mm2. Power=hdg*v h=height d=density g=acc. Due to gavity v=velocity(here = rate of flow of blood) ANS is 1.15= 1.2W(TAKE CARE OF THE UNITS)

Ayush Pateria

20 Points

13 years ago

WORK DONE W IS GIVEN BY
W = F X D
F = PA (PRESSURE X AREA)
OR W = P A.D = P (AD) = P V
OR WORK DONE = PRESSURE X VOLUME
HERE PRESSURE P = 130mm OF Hg = 10⁵ * 130/760
OR P = 13 x 10⁵/ 76 Pa
VOLUME V = 4L = 4000 cm³ = 4x10^-3 m³
HENCE W = PV = (13 x 10⁵/ 76 ) x 4x10^-3
OR Wok done = 68.42 JOULES
NOW THE PUMPING OF 4 L OF BLOOD IS DONE IN 1min = 60s
THUS POWER = WORK DONE/TIME
OR POWER = 68.42/60 = 1.1403 WATTS

Vikas TU

14149 Points

13 years ago

P =work /time
f*d/t=f*v(v=velocity)
Assume the area to be 1 mm2.
Power=hdg*v h=height d=density g=acc.
Due to gavity v=velocity(here = rate of flow of blood)
ANS is 1.15= 1.2W

infernape

11 Points

7 years ago

V = volume = 4 L
h = pressure = 130 mm of mercury
p = density = 13.6 gm/cm^3
t = time = 1 minute

The Volume of blood
V = 4 litres
V = 4 x 10^3 cm^3
V = 4 x 10^-3 m^3

Work done is given by the formula --> Force x Distance
Note that Force = Pressure x Area, & Volume = Area x Distance

Therefore:
Work = Force x Distance
Work = Pressure x Area x Distance
Work = Pressure x Volume
Work = (h)(p)(g)(V)

Power is Work "over" time = hpgV / t

We already know:
v = volume = 4 L => 4x10^-3 m^3
h = pressure = 130 mm of mercury => 0.13 m
p = density = 13.6 gm/cm^3 = 13.6x10^3
t = 1 minute => 60 seconds

The extra variable is:
g = gravity = 9.8 m/s^2

Plug these numbers into the Power equation:
Power = hpgV/t
Power = [(0.13)(13.6x10^3)(9.8)(4x10^-3)]/(60)
Power = 69.3056 / 60
Power = 1.155093

Therefore the power of the heart is approximately 1.155 W

Mahendra Chapagain

26 Points

6 years ago

actually:power formula is WORK DONE/TIME

now,

1.work done =force*displacement

=pressure*area*displacement (because:pressure=force/area)

=height*density*gravity*area*displacement (in context of liquid pressure p=hdg)

=HDGV finally (because area*displacement taken as volume)

2.time taken

at last formula of power=HDGV/T

solving

(0.13*13.6*1000*9.8*4/1000)60

ans:1.155 i.e.1.2 watt

Rishi Sharma

askIITians Faculty 646 Points

3 years ago

Dear Student,
Please find below the solution to your problem.

P = work /time f*d/t
= f*v (v=velocity)
Assume the area to be 1 mm2.
Power = hdg*v
h = height
d = density
g = acc.
Due to gavity v = velocity(here = rate of flow of blood)
ANS is 1.15= 1.2W

Thanks and Regards