Fluid Mechanics Open Channel Problem

In summary, to solve for the slope that will produce a flow rate of 5.66 m^3/s in a trapezoidal canal with a bottom width of 6.10m and side slopes of 1 on 1, the Manning formula can be used. The allowable average velocity of 0.76 m/s and the roughness coefficient of 0.030 are also given. Using the formula V=(1.486/n)R^2/3 x S^1/2 and the known values, the slope can be determined by solving for S. The book's answer is 0.000675.
  • #1
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The problem: A canal cut in rock (n= 0.030) is a trapezoidal in section with a bottom width of 6.10m and the side slopes of 1 on 1. The allowable average velocity is 0.76 m/s. What slope will produce 5.66 m^3/s? The books answer is 0.000675

from the mannings equation

V=(1.486/n)R^2/3 x S^1/2 i get... 0.76=(1.486/0.030)? I am confused on where to go
 
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  • #2
Use of the Manning formula necessitates knowing the slope. But that is what is sought. So how did you do justify you did?

Hint:
Start out by determining the area of the open channel. Then use the Manning formula to determine the slope.
 

What is fluid mechanics?

Fluid mechanics is a branch of physics that deals with the study of fluids (liquids and gases) and their behavior when subjected to different forces and conditions. It involves the study of how fluids flow, how they interact with their surroundings, and how they can be controlled and manipulated.

What is an open channel problem in fluid mechanics?

An open channel problem in fluid mechanics refers to the study of how fluids flow in an open channel, such as a river, canal, or pipe with an open surface. It involves understanding the dynamics of the fluid, the forces acting on it, and the factors that affect its flow rate and behavior.

What are some common applications of open channel problems in fluid mechanics?

Open channel problems in fluid mechanics have various applications in engineering and environmental sciences. Some common examples include the design and management of irrigation systems, flood control systems, and wastewater treatment plants. It is also used in the study of river and coastal hydrodynamics, as well as in the design of water supply and drainage systems.

What are the main challenges in solving open channel problems in fluid mechanics?

The main challenges in solving open channel problems in fluid mechanics include accurately modeling the complex flow patterns and interactions between the fluid and its surroundings, taking into account factors such as surface tension, viscosity, and turbulence. Additionally, the geometry and topography of the channel can also significantly affect the flow behavior, making it challenging to predict and control.

What are some common methods used to solve open channel problems in fluid mechanics?

There are various numerical, analytical, and experimental methods used to solve open channel problems in fluid mechanics. These include the use of computational fluid dynamics (CFD) simulations, mathematical equations and models, and physical experiments using scaled-down models or prototypes. The choice of method depends on the specific problem and the level of accuracy required.

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