The question statement does not call the 4cm depth. But then, I'm not sure what the 4cm is supposed to represent. It seems to be the effective width of the flow, i.e. the region that's redirected by the wedge. The diagram make it look narrower than the wedge, which surprises me.princejan7 said:I am just wondering if the 4cm is called depth, then what is the term for the "into the paper" dimension
That is taken into account by the 4cm width.princejan7 said:Also, shouldn't there be two "v cos (theta/2)" terms in the x momentum expression since there are two streams leaving the control volume?
haruspex said:The question statement does not call the 4cm depth. But then, I'm not sure what the 4cm is supposed to represent. It seems to be the effective width of the flow, i.e. the region that's redirected by the wedge. The diagram make it look narrower than the wedge, which surprises me.
In time t, what volume goes by (width w, depth d, velocity v)?princejan7 said:could you also explain why mass flow rate per unit depth is calculated as density x velocity x 4cm
haruspex said:In time t, what volume goes by (width w, depth d, velocity v)?
Chestermiller said:Let's suppose that the depth is d. Then the cross section of the channel perpendicular to the flow is 0.04d. The volumetric flow rate in the upstream region Q through this cross section is the fluid velocity times the area. So Q = 6(0.04)d. The mass flow rate is ρQ=6ρ(0.04)d.
In the region of the wedge, if the velocity is still 6 m/s, each channel surrounding the wedge has an opening (width) of 2 cm. This guarantees that the mass flow rate is conserved.
Chet
That is taken into account by the 4cm width.
It's the combined (effective) width of the two streams, so it's included in the mass flow rate.princejan7 said:How does the 4cm take into account the other stream; the second "mass flow rate* V *cos(theta/2)" term
princejan7 said:How does the 4cm take into account the other stream; the second "mass flow rate* V *cos(theta/2)" term
Momentum relation for control volume is a fundamental concept in fluid mechanics that describes the relationship between the forces acting on a fluid and the resulting change in momentum within a specific volume of the fluid. It is based on the law of conservation of momentum, which states that the total momentum of a closed system remains constant unless acted upon by an external force.
The momentum relation for control volume is derived from the Navier-Stokes equations, which are the governing equations for fluid flow. These equations are based on the principles of conservation of mass, momentum, and energy, and can be applied to any fluid flow situation. By applying these equations to a control volume, we can determine the change in momentum within that volume due to external forces.
The momentum relation for control volume is important because it allows us to analyze and predict the behavior of fluids in various engineering applications. By understanding the forces and changes in momentum within a control volume, we can design systems and structures that can withstand or control the forces of fluid flow.
The momentum relation for control volume is based on certain assumptions, such as the fluid being incompressible and the flow being steady and laminar. These assumptions may not hold true in all fluid flow situations, and thus the results obtained from the momentum relation may not be entirely accurate. Additionally, the momentum relation does not take into account the effects of turbulence, which can significantly impact the behavior of fluids.
The momentum relation for control volume is widely used in various engineering fields, such as aerospace, mechanical, and civil engineering. It is applied in the design of pumps, turbines, and other fluid machinery, as well as in the analysis of fluid flow in pipes, channels, and other structures. It is also used in the design of vehicles, such as airplanes and ships, to ensure their stability and performance in various fluid flow conditions.