A pipe carrying 20°C water has a diameter of 3.6 cm. Estimate the maximum flow speed if the flow must be streamline.
Answer in cm/s
To estimate the maximum flow speed of streamline water in a pipe, we can consider the concept of flow rate. The flow rate is the volume of fluid passing through a given point per unit time.
The formula for flow rate (Q) is Q = A × V, where A represents the cross-sectional area of the pipe and V represents the flow speed.
To calculate the flow speed (V), we need to rearrange the formula as follows: V = Q / A.
First, we need to calculate the cross-sectional area of the pipe. The formula for the area of a circle is A = π × r², where r represents the radius of the pipe.
Given that the diameter (d) of the pipe is 3.6 cm, we can find the radius (r) by dividing the diameter by 2: r = d / 2.
Now we can calculate the cross-sectional area (A) of the pipe using the radius (r) we just found.
A = π × (r)²
Next, we need to estimate the flow rate (Q). For this question, we are only provided with the temperature of the water. However, the flow rate also depends on other factors like pressure difference or the inclination of the pipe, which are not given. Thus, we cannot estimate the flow rate accurately.
However, since the question asks for the maximum flow speed, we can assume that there are no significant restrictions or obstacles in the pipe. In this case, we can consider the maximum flow speed to be the speed of sound in water, which is approximately 1482 m/s.
Now, we can substitute the calculated values into the formula V = Q / A to find the maximum flow speed:
V = (1482 m/s) / A
Since the answer is required in cm/s, we need to convert the flow speed from m/s to cm/s by multiplying by 100:
V = (1482 m/s) × 100 cm/m = 148,200 cm/s
Therefore, the estimated maximum flow speed of streamline water in the given pipe is 148,200 cm/s.