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Calculate the flow rate of blood in cubic meters per second, given a heart rate of 10 beats/minute and a stroke volume of 0.04 liters/beat.

Physics

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Answer

6.67×10−6 m3/s6.67 \times 10^{-6}\,\text{m}^3/\text{s}

Step-by-step solution

5 steps

  1. Identify the given values.

    Volume of blood pumped per beat = 0.04 liters/beat0.04\,\text{liters/beat}.
    Heart rate = 10 beats/minute10\,\text{beats/minute}.

  2. Calculate the total volume of blood pumped per minute.

    Total volume per minute = (Volume per beat) ×\times (Heart rate)

    =0.04 litersbeat×10 beatsminute= 0.04\,\frac{\text{liters}}{\text{beat}} \times 10\,\frac{\text{beats}}{\text{minute}} =0.4 litersminute= 0.4\,\frac{\text{liters}}{\text{minute}}

  3. Convert the volume from liters to cubic meters.

    We know that 1 liter=0.001 m31\,\text{liter} = 0.001\,\text{m}^3.

    0.4 liters=0.4×0.001 m3=0.0004 m30.4\,\text{liters} = 0.4 \times 0.001\,\text{m}^3 = 0.0004\,\text{m}^3

    So, the flow rate is 0.0004 m3minute0.0004\,\frac{\text{m}^3}{\text{minute}}.

  4. Convert the time from minutes to seconds.

    We know that 1 minute=60 seconds1\,\text{minute} = 60\,\text{seconds}.
    To convert m3minute\frac{\text{m}^3}{\text{minute}} to m3second\frac{\text{m}^3}{\text{second}}, we divide by 60.

    Flow rate=0.0004 m31 minute=0.0004 m360 s\text{Flow rate} = \frac{0.0004\,\text{m}^3}{1\,\text{minute}} = \frac{0.0004\,\text{m}^3}{60\,\text{s}}

  5. Calculate the final flow rate in cubic meters per second.

    Flow rate=0.000460 m3s\text{Flow rate} = \frac{0.0004}{60}\,\frac{\text{m}^3}{\text{s}} Flow rate≈0.0000066667 m3s\text{Flow rate} \approx 0.0000066667\,\frac{\text{m}^3}{\text{s}}

    We can express this in scientific notation:

    Flow rate≈6.67×10−6 m3s\text{Flow rate} \approx 6.67 \times 10^{-6}\,\frac{\text{m}^3}{\text{s}}

    The flow rate is approximately 6.67 x 10−6^{-6} m3^3/s.

    6.67×10−6 m3/s6.67 \times 10^{-6}\,\text{m}^3/\text{s}
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