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R is the pipe radius, A is the cross-sectional area of pipe. The equation does not hold close to the pipe entrance. [8]: 3 The equation fails in the limit of low viscosity, wide and/or short pipe. Low viscosity or a wide pipe may result in turbulent flow, making it necessary to use more complex models, such as the Darcy–Weisbach equation.
The Borda–Carnot equation is applied to the flow through a sudden expansion of a horizontal pipe. At cross section 1, the mean flow velocity is equal to v 1, the pressure is p 1 and the cross-sectional area is A 1.
A is the cross-sectional area of the flow, P is the wetted perimeter of the cross-section. More intuitively, the hydraulic diameter can be understood as a function of the hydraulic radius R H, which is defined as the cross-sectional area of the channel divided by the wetted perimeter. Here, the wetted perimeter includes all surfaces acted upon ...
In the case of a non-circular cross-section of a pipe, the same formula can be used to find the entry length with a little modification. A new parameter “hydraulic diameter” relates the flow in non-circular pipe to that of circular pipe flow. This is valid as long as the cross-sectional area shape is not too exaggerated.
Let the x axis be directed down the axis of the pipe. Define a parcel of fluid moving through a pipe with cross-sectional area A, the length of the parcel is dx, and the volume of the parcel A dx. If mass density is ρ, the mass of the parcel is density multiplied by its volume m = ρA dx.
The flow rate can be converted to a mean flow velocity V by dividing by the wetted area of the flow (which equals the cross-sectional area of the pipe if the pipe is full of fluid). Pressure has dimensions of energy per unit volume, therefore the pressure drop between two points must be proportional to the dynamic pressure q.
Diagram showing definitions and directions for Darcy's law. A is the cross sectional area (m 2) of the cylinder. Q is the flow rate (m 3 /s) of the fluid flowing through the area A. The flux of fluid through A is q = Q/A. L is the length of the cylinder. Δp = p outlet - p inlet = p b - p a.
At initially subsonic upstream conditions, the conservation of energy principle requires the fluid velocity to increase as it flows through the smaller cross-sectional area of the constriction. At the same time, the venturi effect causes the static pressure, and therefore the density, to decrease at the constriction.