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Describe the relationship between flow rate and velocity. Explain the consequences of the equation of continuity to the conservation of mass. The first part of this chapter dealt with fluid statics, the study of fluids at rest. The rest of this chapter deals with fluid dynamics, the study of fluids in motion.
Bernoulli’s equation states that the sum on each side of the following equation is constant, or the same at any two points in an incompressible frictionless fluid: $$p_{1} + \frac{1}{2} \rho v_{1}^{2} + \rho gh_{1} = p_{2}+ \frac{1}{2} \rho v_{2}^{2} + \rho gh_{2} \ldotp$$
Bernoulli’s equation states that the sum on each side of the following equation is constant, or the same at any two points in an incompressible frictionless fluid: \[P_1 + \dfrac{1}{2}\rho v_1^2 + \rho gh_1 = P_2 + \dfrac{1}{2}\rho v_2^2 + \rho gh_2.\]
What is Bernoulli's equation? Applying Bernoulli's equation. Finding flow rate from Bernoulli's equation.
ρ = fluid mass density; u is the flow velocity vector; E = total volume energy density; U = internal energy per unit mass of fluid; p = pressure; denotes the tensor product
Momentum Equation for Inertial Control Volume with Rectilinear Acceleration For a Newtonian fluid: Shear Stress = Where μ is the dynamic viscosity of the fluid.
The cornerstone of computational fluid dynamics is the fundamental governing equations of fluid dynamics—the continuity, momentum and energy equations. These equations speak physics. They are the mathematical statements of three fun-damental physical principles upon which all of fluid dynamics is based: (1) mass is conserved;
