find a detailed question in the attached word doc file

A continuous wave ultrasonic flow meter has a transmitted and receiver side by side with an effective angle between them of 0o . The probe axis makes an angle θ with the blood vessel being insonated. The blood flow is towards the probe, though not along the axis of the probe.

• Derive from the first principles the complete frequency/ velocity (Doppler) relationship

(Mathematical Expression)

defining all your terms.

• How big would vs have to be before fD is overestimated by 1%? Is this condition likely to arise?

• The probe effectively measure the component of velocity towards the probe. To correctly estimate vs the angle θ needs to be known. Although the angle to the skin surface can be measured, the angle to the vessel is generally unknown.

Assume that the position of the probe in space (position and direction of the axis) can be measured. Suggest a way of using two measurements to determine the velocity along the axis of the blood vessel.

Note: Mathematical expression is in the attached doc file