Calculate the flow rate of blood (of density 1.03 g/cm3) in an aorta with a cross-sectional area of 2.88 cm2
if the flow speed is 28.5 cm/s. Answer in units of g/s.
28.5 cm/s * 2.88 cm^2 = 82.1 cm^3/s volume flow rate
so mass flow rate is
82.1 cm^3/s * 1.03 g/cm^3 = 84.5 g/s
Thanks!
Why did the blood go to therapy? Because it had flow issues!
To calculate the flow rate of blood, we can multiply the cross-sectional area of the aorta by the flow speed of the blood.
Cross-sectional area (A) = 2.88 cm²
Flow speed (V) = 28.5 cm/s
The flow rate (Q) can be calculated using the formula:
Q = A * V
Substituting the given values:
Q = 2.88 cm² * 28.5 cm/s
Now let's convert the units properly:
1 cm² = 0.01 m²
1 cm/s = 0.01 m/s
Q = (2.88 cm² * 0.01 m²/cm²) * (28.5 cm/s * 0.01 m/s/cm/s)
Q = 0.0288 m² * 0.285 m/s
Q ≈ 0.008208 m³/s
Since the density of the blood is given as 1.03 g/cm³, we can calculate the flow rate in grams per second:
Flow rate (Q) = Volume (V) * Density (ρ)
Q = 0.008208 m³/s * 1.03 g/cm³ * 1000 cm³/m³
Q ≈ 8.45264 g/s
Therefore, the flow rate of blood in the aorta is approximately 8.45 g/s.
To calculate the flow rate of blood, you can use the formula:
Flow Rate = Cross-sectional Area × Flow Speed
Given:
Density of blood (ρ) = 1.03 g/cm³
Cross-sectional Area (A) = 2.88 cm²
Flow Speed (v) = 28.5 cm/s
First, let's convert the cross-sectional area from cm² to m²:
1 cm² = (1/100) m²
So, Cross-sectional Area (A) in m² = 2.88 cm² × (1/100) m²/cm²
Now we can calculate the flow rate using the formula:
Flow Rate = A × v = (2.88 cm² × (1/100) m²/cm²) × 28.5 cm/s
Flow Rate = 2.88 × 28.5 × (1/100) g/s
Calculating the value:
Flow Rate = 0.82176 g/s
Therefore, the flow rate of blood in the aorta is approximately 0.82176 g/s.
To calculate the flow rate of blood in the aorta, you will need to use the formula:
Flow Rate = Volume / Time
In this case, the volume of blood passing through the aorta is equivalent to the product of the cross-sectional area and the flow speed:
Volume = Cross-sectional Area × Flow Speed
Before proceeding, you need to convert the given flow speed from cm/s to m/s to ensure consistent units. Since 1 m = 100 cm and 1 s = 1 s, you can convert cm/s to m/s by dividing the value by 100:
Flow Speed (m/s) = 28.5 cm/s / 100 = 0.285 m/s
Now, substitute the values for volume and time in the flow rate formula:
Flow Rate = (Cross-sectional Area × Flow Speed) / Time
The density of blood is given as 1.03 g/cm^3. However, the flow rate is usually expressed in units of mass per unit time (g/s). To convert the volume (cm^3) to mass (grams), you can multiply by the density:
Flow Rate = (Cross-sectional Area × Flow Speed × Density) / Time
Substituting the given values:
Flow Rate = (2.88 cm^2 × 0.285 m/s × 1.03 g/cm^3) / Time
At this point, we need the value of time to calculate the flow rate accurately. If you have the time interval over which the blood flow rate is measured, you can substitute it into the equation to find the flow rate in g/s.