Blood is pumped from the heart at a rate of 5L/min into the aorta of radius 2.0cm. Assuming that the density of blood 1x103 kg/m3 .Determine the velocity of blood through

the aorta

Q=vA

Q=5L/min=8.3e-5 m^3/sec
A= pi*r^2=3.14*4*10^-4=0.001256 m2
v=Q/A
v=8.3e-5/0.001256 = 0.006m/sec = 0.6cm/sec

for rate 4.5 L/min and radius r = 1.1 cm

Given

rate of blood pumped from the heart is = 4.5 L/min

we know that 1 L = 1000 cm^3

the flow rate in cm^3/s , by heart is = 4.5*1000/60 cm^3/s = 75 cm^3/s -------------(H)

the area of aorta is A = pi*r^2 = pi*1.1^2 = 3.80132 cm^2

now the rate of flow is A*v ----------(A)

where A is area of aorta and v is speed of blood in aorta

equating (H) to (A) ( from equation of continuity A1*V1 = A2*V2)

75 = A*v

v = 75/A

v = 75/3.80132 cm/s

v = 19.7299885303 cm/s

To determine the velocity of blood through the aorta, we can use the principle of continuity. According to this principle, the flow rate of a fluid remains constant as it passes through different sections of a pipe.

The formula for flow rate is:
Flow Rate = Area × Velocity

In this case, the flow rate of blood is 5 L/min, which can be converted to m^3/s by dividing by 1000 (1 L = 0.001 m^3) and by 60 (1 min = 60 s):
Flow Rate = 5 L/min × (0.001 m^3/L) × (1 min/60 s) = 8.33 × 10^(-5) m^3/s

The area of the aorta can be calculated using the formula for the area of a circle:
Area = π × radius^2
Area = π × (0.02 m)^2 = 4 × 10^(-4) m^2

Now, we can rearrange the formula for flow rate to solve for velocity:
Velocity = Flow Rate / Area
Velocity = (8.33 × 10^(-5) m^3/s) / (4 × 10^(-4) m^2)

Simplifying the expression:
Velocity = 2.08 m/s

Therefore, the velocity of blood through the aorta is 2.08 m/s.

To determine the velocity of blood through the aorta, we can use the principle of conservation of mass.

The formula for the conservation of mass is:
A1v1 = A2v2

Where:
A1 and A2 are the cross-sectional areas of the aorta at two different points
v1 and v2 are the velocities of blood at those two points

We have the following information:
- The blood is pumped from the heart at a rate of 5 L/min, which is equivalent to 5/60 m3/s (since there are 60 seconds in a minute).
- The radius of the aorta is 2.0 cm, which is equivalent to 0.02 m.
- The density of blood is 1x103 kg/m3.

First, let's calculate the cross-sectional area of the aorta at the point where blood is pumped from the heart. We can use the formula for the area of a circle:

A1 = π * r1^2
= π * (0.02 m)^2

Next, let's calculate the velocity of blood at the point where it is pumped from the heart:

v1 = (5/60 m3/s) / A1

Now, we need to determine the cross-sectional area of the aorta. Since the aorta is a tube, its cross-sectional area is constant. Therefore, we can use the area calculated at the point where blood is pumped from the heart.

A2 = A1

Finally, we can calculate the velocity of blood through the aorta at any point:

v2 = (A1 * v1) / A2

Now, let's plug in the values and calculate the velocity:

A1 = π * (0.02 m)^2
v1 = (5/60 m3/s) / A1
A2 = A1
v2 = (A1 * v1) / A2

Once you calculate these values, you will have the velocity of blood through the aorta.