Question

The left ventricle of a resting adult's heart pumps blood at a flow rate of 85.0 cm3/s, increasing its pressure by 110 mm Hg, its velocity from zero to 25.0 cm/s, and its height by 5.00 cm. (All numbers are averaged over the entire heartbeat.) Calculate the total power output (in W) of the left ventricle. Note that most of the power is used to increase blood pressure.

Answer 1

P = 1.29625 W

Step-by-step explanation:

Given

Q = 85.0 cm ³ / s, p₁ = 110 mmHg, u₁ = 25.0 cm / s, h = 5.0 cm

Also knowing the density of the blood is

ρₐ = 1.05 x 10 ³ kg / m³

Δp₁ = 110 mmHg * 133.322 Pa / 1 mmHg

Q = 85.0 cm³ / s = 85.0 x 10 ⁻⁶ m³ / s

To calculated the power

P = H * Q

H = Δp₁ + ¹/₂ * ρₐ * ( u₁² - v₂²) + ρₐ * g *Δh

H = 14.666 x 10 ³ Pa + 0.5 * 1.05 x 10 ³ kg / m³ * ( 25 x 10 ² m /s )² + 1.05 x 10 ³ kg / m³ * 9.8 m /s² * 0.05 m

H = 15.25 x 10 ³ Pa

P = 15.25 x 10 ³ Pa * 85.0 x 10 ⁻⁶ m³ / s

P = 1.29625 W