If the heart pumps blood into the aorta, the pressure gradient-the difference among the blood pressure within the heart and the blood pressure in the artery-is a significant diagnostic measurement. A direct measurement of the pressure gradient is complicated; however an indirect determination can be made through measuring the Doppler shift of reflected ultrasound. Blood is fundamentally at rest in the heart; if it leaves and enters the aorta, it speeds up considerably and according to Bernoulli's equation-the pressure must reduce. A doctor employing ultrasound of 2.5 measures a 5900 frequency shift as the ultrasound reflects from the blood ejected from the heart.
i) Determine the speed of the blood in the aorta? Suppose that the speed of sound in human body is around 1540.
ii) Determine the difference in blood pressure among the inside of the heart and the aorta? Suppose that the patient is lying down and that there is no difference in height as the blood moves from the heart to the aorta.