Answer:
Performing the calculations:
A ≈ 0.0045238934 m²
v ≈ 11.041 m/sec (approximately)
Step-by-step explanation:
To calculate the velocity in the vessel, we need to convert the flow rate from cm³/sec to m³/sec and calculate the cross-sectional area of the vessel. With these values, we can then determine the velocity using the equation:
Velocity (v) = Flow rate (Q) / Cross-sectional area (A)
Given:
Flow rate (Q) = 50 cm³/sec
Radius (r) = 12 mm
First, let's convert the flow rate from cm³/sec to m³/sec:
Q = 50 cm³/sec = 50 * (1/1000) m³/sec = 0.05 m³/sec
Next, we can calculate the cross-sectional area of the vessel using the radius:
A = π * (r^2)
Now, let's calculate the velocity:
v = Q / A
Given that the radius (r) is in millimeters, we need to convert it to meters before performing the calculation.
Let's proceed with the calculations:
Given:
Flow rate (Q) = 0.05 m³/sec
Radius (r) = 12 mm = 0.012 m
Calculate the cross-sectional area (A):
A = π * (r^2)
Calculate the velocity (v):
v = Q / A
Performing the calculations:
A ≈ 0.0045238934 m²
v ≈ 11.041 m/sec (approximately)