Horizontal Tube Speed

In summary, the problem at hand involves seawater flowing through two horizontal tubes of different diameters, with a pressure difference of 7.25 kPa between them. The question is asking for the speed of flow in the first tube. Initially, the equation P1 + 1/2 pv2 was thought to be applicable, but it was later discovered that this was not the case. The conversation then discusses the use of the conservation of mass and Bernoulli's equation to solve the problem.
  • #1
Hypnos_16
153
1

Homework Statement



Seawater flows through a horizontal tube of diameter 3.00 cm that is joined to a second horizontal tube of diameter 1.70 cm. The pressure difference between the tubes is 7.25 kPa. What is the speed of flow in the first tube?

Homework Equations



I thought it was P1 + 1/2 pv2
turns out it isn't

The Attempt at a Solution



i don't know if it's cause I'm stressed, or just missing something, i cannot get this question to work.
 
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  • #2
Note: P1 + 1/2 p v1^2 = constant = P2 + 1/2 pv2^2.

Do you also need to apply the conservation of mass ?
 
  • #3
The conservation of mass? and what "Constant" are you talking about there?
 
  • #4
The conservation of mass will allow you to relate the speed of the fluid in the two different size pipes and the pipe diameter.

Bernoulli's equation says P + p v^2 / 2 + p g h = constant. So if you know these values at one point, you know them at the other.
 
  • #5


As a scientist, it is important to approach problems with a calm and logical mindset. In this case, the given information is not enough to determine the speed of flow in the first tube. The equation provided, P1 + 1/2 pv2, is not applicable in this scenario as it is for Bernoulli's equation, which requires additional information such as the density of the fluid and the height difference between the two points.

To solve this problem, we need to use the continuity equation, which states that the volume flow rate through a pipe is constant. In this case, we can set the volume flow rate in the first tube equal to the volume flow rate in the second tube.

Q1 = Q2

To find the volume flow rate, we can use the equation Q = Av, where A is the cross-sectional area of the tube and v is the velocity of flow.

Q1 = A1v1

Q2 = A2v2

Since the tubes are connected, the cross-sectional area must be the same. Therefore, we can set A1 = A2.

Q1 = Q2

A1v1 = A2v2

Since we are looking for the speed of flow in the first tube, we can rearrange the equation to solve for v1.

v1 = (A2/A1)v2

We can also use the equation for pressure difference, ΔP = ρgh, where ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height difference between the two points.

ΔP = ρgh

We can rearrange this equation to solve for the height difference, h = (ΔP/ρg).

Since the tubes are horizontal, the height difference is equal to the length of the tubes. Therefore, we can set h1 = h2.

h1 = h2

(ΔP1/ρg) = (ΔP2/ρg)

Substituting in the given values, we can solve for the height difference.

(7.25 kPa/ρg) = (7.25 kPa/ρg)

Now, we can use this height difference to find the velocity of flow in the second tube using the equation v2 = √(2gh).

Substituting in the calculated height difference and solving for v2,
 

1. What is horizontal tube speed?

Horizontal tube speed refers to the velocity at which a tube or cylindrical object is moving in a horizontal direction. It is typically measured in meters per second (m/s) or kilometers per hour (km/h).

2. How is horizontal tube speed calculated?

Horizontal tube speed is calculated by dividing the distance traveled by the time it takes to travel that distance. This can be represented by the formula: speed = distance / time.

3. What factors can affect horizontal tube speed?

The main factors that can affect horizontal tube speed are the force applied to the tube, the mass of the tube, and any external forces such as friction or air resistance. The shape and surface of the tube can also have an impact on its speed.

4. Why is horizontal tube speed important?

Horizontal tube speed is important in various fields such as physics, engineering, and sports. It helps us understand the motion of objects and can be used to design efficient systems, such as pipelines or roller coasters. In sports, horizontal tube speed can determine the outcome of races and competitions.

5. How can horizontal tube speed be increased?

Horizontal tube speed can be increased by applying a greater force to the tube, reducing its mass, or minimizing external forces such as friction. Additionally, optimizing the shape and surface of the tube can also help increase its speed.

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