Calculating Acceleration Rate in a Decreasing Pipe

In summary, the problem involves a pipe with a decreasing cross sectional area, a given volume flow rate, and a given length. The question asks for the acceleration rate at a specific point and time, as well as the total acceleration rate at that same point if the volume flow rate increases at a certain rate. To solve this, one could potentially use the equation ax = du/dt and plug in the given values to determine the acceleration rate.
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Homework Statement


A pipe is designed to have its cross sectional area decreasing linearly from 12-inch diameter to 6-inch diameter. What is the acceleration rate at a section 10 inches from the ending section of 12-inch pipe at time = 3 sec? The volume flow rate Q=2t cfs (note: t is in sec). Also given is the length of pipe from the 12-inch diameter to the 6-inch diameter is 30-inches.

Homework Equations


Might use ax = du/dt

The Attempt at a Solution


Tried solving Q by letting t=3 and substituting into the Q equation to get 6 cfs, but it hasn't led me any where.
 
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I have a similar question in my Fluid Mechanics book.
Diameter of duct changes linearly over a length of 3m, being 0.46m at entry and 0.15m at outlet. If flow is steady and volume rate of flow is 0.3m^3/s, determine rate of acceleration of fluid at a point halfway along duct.
Determine total rate of acceleration at same point if volume rate of flow increases at 0.37m^3/s^2.

How do you calculate this?
 

1. How do you calculate the acceleration rate in a decreasing pipe?

To calculate the acceleration rate in a decreasing pipe, you will need to use the Bernoulli's equation, which states that the sum of kinetic energy, potential energy, and pressure energy at two different points in a pipe must be equal. By rearranging this equation, you can solve for the acceleration rate.

2. What factors affect the acceleration rate in a decreasing pipe?

The acceleration rate in a decreasing pipe is affected by several factors, including the diameter of the pipe, the velocity of the fluid, and the angle of the pipe. Additionally, the viscosity of the fluid and any external forces, such as gravity, can also impact the acceleration rate.

3. How does the acceleration rate change in a decreasing pipe compared to a constant diameter pipe?

In a constant diameter pipe, the acceleration rate remains constant throughout the pipe. However, in a decreasing pipe, the acceleration rate will increase as the diameter decreases. This is because the fluid must travel through a smaller area, resulting in a higher velocity and therefore a higher acceleration rate.

4. Can the acceleration rate in a decreasing pipe ever be negative?

No, the acceleration rate in a decreasing pipe can never be negative. This is because the fluid is always accelerating in the direction of the flow, even if the velocity is decreasing. Therefore, the acceleration rate will always be a positive value.

5. How does the acceleration rate affect the flow rate in a decreasing pipe?

The acceleration rate and flow rate in a decreasing pipe are inversely proportional. This means that as the acceleration rate increases, the flow rate decreases. This is because a higher acceleration rate means the fluid is moving faster, so it will take less time for the same amount of fluid to flow through the pipe.

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