An apparatus comprising: a dialysis machine including a pump and a filter; an elastomeric tubing in which the blood flows from the patient to said dialysis machine as drawn by said pump; a measuring head having an elongated slot with walls between which said tubing is placed to be held, said slot walls having a transverse length along the slot length which deforms said tubing in said slot, and said slot having first and second points of different transverse length at two locations spaced apart along said slot length; a source of ultrasonic signal energy; a respective first and second transmit/receive sensor (30A, 30B) mounted in said measuring head adjacent said slot first and second points, each said sensor for transmitting ultrasonic signal energy from said source along a respective path through a wall of said tubing and the blood flowing therein, the first receive sensor receiving signals by the first transmit sensor reflected from the internal wall of said tubing back to said first receive sensor, and the second receive sensor receiving signals by the second transmit sensor reflected from the internal wall of said tubing back to a second receive sensor; a temperature sensor mounted to said head for measuring the temperature of the blood flowing in said tubing without contacting the flowing fluid; and a circuit configured for: measuring for each said first and second sensor (30A, 30B) the round-trip transit time of the signals from time of transmission to the time of reception after reflection from said tubing internal wall, calculating a sound velocity of the blood flowing in the tubing based on the two measured round trip transit times and the differential of said slot transverse length at said first and second points, and calculating the blood hematocrit constituent level based on the calculated sound velocity and the temperature measured by said temperature sensor. a dialysis machine including a pump and a filter; an elastomeric tubing in which the blood flows from the patient to said dialysis machine as drawn by said pump; a measuring head having an elongated slot with walls between which said tubing is placed to be held, said slot walls having a transverse length along the slot length which deforms said tubing in said slot, and said slot having first and second points of different transverse length at two locations spaced apart along said slot length; a source of ultrasonic signal energy; a respective first and second transmit/receive sensor (30A, 30B) mounted in said measuring head adjacent said slot first and second points, each said sensor for transmitting ultrasonic signal energy from said source along a respective path through a wall of said tubing and the blood flowing therein, the first receive sensor receiving signals by the first transmit sensor reflected from the internal wall of said tubing back to said first receive sensor, and the second receive sensor receiving signals by the second transmit sensor reflected from the internal wall of said tubing back to a second receive sensor; a temperature sensor mounted to said head for measuring the temperature of the blood flowing in said tubing without contacting the flowing fluid; and a circuit configured for: measuring for each said first and second sensor (30A, 30B) the round-trip transit time of the signals from time of transmission to the time of reception after reflection from said tubing internal wall, calculating a sound velocity of the blood flowing in the tubing based on the two measured round trip transit times and the differential of said slot transverse length at said first and second points, and calculating the blood hematocrit constituent level based on the calculated sound velocity and the temperature measured by said temperature sensor. measuring for each said first and second sensor (30A, 30B) the round-trip transit time of the signals from time of transmission to the time of reception after reflection from said tubing internal wall, calculating a sound velocity of the blood flowing in the tubing based on the two measured round trip transit times and the differential of said slot transverse length at said first and second points, and calculating the blood hematocrit constituent level based on the calculated sound velocity and the temperature measured by said temperature sensor.