blood is pumped from the heart at a rate of 5.0l/min into the aorta (radius 1.0cm)determinethethe speed of the blood
volume=area*distance
volume/time=area*distance/time
distance/time=speed=5dm^3/sec /(Pi r^2)
since you units on volume are decimeter, change radius for cm to dm, or r=.1dm
speed=5dm^3/(PI*.1^2 dm^2)
that give you speed in dm/min
now if you want cm/sec, multiply by 10
To determine the speed of the blood, we can use the equation of continuity, which states that the product of cross-sectional area and velocity of fluid is constant. In this case, we can use the cross-sectional area of the aorta to find the velocity.
First, let's convert the radius of the aorta to meters. The radius is given as 1.0 cm, so it is 0.01 meters.
Next, we will calculate the cross-sectional area of the aorta using the formula A = πr^2, where A represents the cross-sectional area and r is the radius.
A = π * (0.01 m)^2 = 0.000314 m^2
Now, let's use the equation of continuity, which is A1v1 = A2v2. In this case, A1 is the cross-sectional area of the aorta, v1 is the speed of blood, A2 is the cross-sectional area at another point (which we don't know), and v2 is the speed of blood at that point.
We have the following values:
A1 = 0.000314 m^2
v1 = 5.0 L/min
Since the speed of blood is given as liters per minute, we need to convert it to cubic meters per second. To do this, we divide by 1000 (to convert liters to cubic meters) and by 60 (to convert minutes to seconds):
v1 = 5.0 L/min * (1 m^3 / 1000 L) * (1 min / 60 s) = 8.33 × 10^-5 m/s
Now we can rearrange the equation of continuity to solve for v2:
A2v2 = A1v1
v2 = (A1v1) / A2
Since the cross-sectional area at the other point is not given, we cannot find the exact speed of blood at that point.