Water Flow Speed: Diameter 0.2mm to 5mm

• mikefitz
In summary, the diameter of a tube has a direct impact on the speed of water flow, with smaller diameters resulting in higher speeds. The relationship between water flow speed and tube diameter is inverse, and there is an optimal diameter for maximum water flow speed known as the critical diameter. The viscosity of water also affects the water flow speed in a tube, with higher viscosities resulting in slower speeds. Other factors such as length, material, surface roughness, and obstructions can also affect water flow speed in a tube.
mikefitz
Water entering a house flows with a speed of 0.22 m/s through a pipe of 2.3 cm inside diameter. What is the speed of the water at a point where the pipe tapers to a diameter of 5 mm in m/s?

Area 1 = 4.155
Area 2 = 19.635

Flow 1 = 4.155 (.22) = .914 m/s
.914 = 19.635v
v=.04655 mm/s

convert .04655 mm/s to m/s = 465500m/s - woah, wrong! any ideas?

dude ur area is wrong the diameters are 2.3 CM and 5 MM but u calculate ur area in mm^2 for both !

I would first like to clarify the units provided in the question. The diameter range of 0.2mm to 5mm suggests a very small scale, while the flow speed of water entering a house at 0.22 m/s suggests a much larger scale. It is important to ensure that the units are consistent in order to accurately calculate the speed of the water at the tapered point.

Assuming that the units for the diameter range are in millimeters (mm) and the flow speed is in meters per second (m/s), we can proceed with the calculation.

First, we need to calculate the cross-sectional area at both points using the formula A = πr^2, where r is the radius of the pipe.

At the initial point where the diameter is 2.3 cm (or 23 mm), the radius would be 11.5 mm. Therefore, the cross-sectional area would be A1 = π(11.5)^2 = 415.3 mm^2.

At the tapered point where the diameter is 5 mm, the radius would be 2.5 mm. Therefore, the cross-sectional area would be A2 = π(2.5)^2 = 19.6 mm^2.

Next, we can use the equation Q = Av, where Q is the volumetric flow rate, A is the cross-sectional area, and v is the speed of the water.

At the initial point, we know the flow rate (Q) is 0.22 m/s and the cross-sectional area (A1) is 415.3 mm^2 (0.0004153 m^2). Therefore, we can solve for v1 as:

0.22 m/s = (0.0004153 m^2)v1
v1 = 0.22/0.0004153 = 530.1 m/s

At the tapered point, we know the cross-sectional area (A2) is 19.6 mm^2 (0.0000196 m^2). Therefore, we can solve for v2 as:

v2 = 0.22/0.0000196 = 11224.5 m/s

This result seems very high and unrealistic, which may indicate an error in the units provided. If we assume that the units for the flow speed were meant to be in mm/s instead of m/s, the calculation would yield a more

1. How does the diameter of a tube affect the speed of water flow?

The diameter of a tube has a direct impact on the speed of water flow. Generally, the smaller the diameter, the higher the speed of water flow. This is because a smaller diameter creates a higher pressure, which pushes the water through the tube at a faster rate.

2. What is the relationship between water flow speed and tube diameter?

The relationship between water flow speed and tube diameter is inverse. This means that as the tube diameter decreases, the water flow speed increases. Conversely, as the tube diameter increases, the water flow speed decreases.

3. Is there an optimal diameter for maximum water flow speed?

Yes, there is an optimal diameter for maximum water flow speed. This is known as the critical diameter, which is the diameter at which the water flow speed is at its maximum. This diameter is specific to each tube and is affected by factors such as viscosity and surface tension of the water.

4. How does the viscosity of water affect the water flow speed in a tube?

The viscosity of water is a measure of its resistance to flow. As a result, the higher the viscosity, the slower the water flow speed in a tube. This means that for a given tube diameter, water with a higher viscosity will flow through it at a slower rate compared to water with a lower viscosity.

5. Can other factors besides diameter affect water flow speed in a tube?

Yes, there are other factors besides diameter that can affect water flow speed in a tube. These include the length of the tube, the material of the tube, the surface roughness of the tube, and any obstructions or bends in the tube. These factors can either increase or decrease the water flow speed in a tube.

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