A CW ultrasonic Doppler flowmeter is used to measure blood flow in a carotid artery with a peak velocity of 100 cm/s and a radius of 0.5 cm. The velocity profile in the vessel is assumed to be parabolic. Suppose that the flowmeter is designed to measure the mean Doppler shift frequency. What is the mean frequency for a Doppler angle of 450 and a carrier frequency of 8 MHz? Another ultrasound method for measuring blood flow velocity, called transit time ultrasonic flowmeter, is shown in the accompanied figure. The velocity can be estimated by measuring the transit times of an ultrasound pulse propagating upstream and downstream. Show that the difference in transit times between upstream and downstream propagation is given by if c, sound velocity in blood >>V.
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