Given
Continuity equation
Where
Applying in the continuity equation
We need to find
So the solution is
1. The equation of continuity of a pure fluid is given as др at + V.pv...
In addition, derive the "wave equation" for an incompressible
fluid. Use the continuity equation and the linearized euler
equation.
Linearized Euler:
A flow is incompressible if a fluid element does not change its density as the element moves. From Problem 54.1, this means (7p/dt) u . ρ-0. (a) Show that for an incompressible fluid the equation of continuity reduces to V -u -0. (b) Write Euler's equation for the flow of an incompressible fluid. (c) What is c for an...
1.) Continuity Equation (3 Pkt.) Demonstrate that it is possible to write the continuity equation in the form dt Show that this is equal to the form: dt Derive a diagnostic equation for the vertical wind component w(z) with the assumption of large scale movements.
Problem 3. Consider a pipe containing a steadily flowing inviscid fluid. It has one inlet and branches into two arms so that there are two outlets (see Fig. 1). Flow can be considered uniform and parallel to the walls when entering and exiting the pipe Inlet Pi Outlet ρ2 A2 p, Outlet Figure 1: Flow of fluid through a "T" -junction in a pipe, shown from above (not to scale) Part A (a) The Continuity equation, as given on the...
Advanced Fluid Mechanics
For an inviscid fluid we have Euler's equation (vectors are denoted by bold characters) )= Vp - Vgx + V xu at and whether or not the fluid is incompressible, we also have the conservation of mass Dp +pv u 0. Dt Show that x Vp Dt Deduce that, if p is a function of palone, the vorticity equation is exactly as in the incompressible, constant density case, except that ois replaced by ap.
For an inviscid...
#1 The Equation of Continuity: Consider Figure 1 which illustrates a small mathernat ical box in a fluid. The basic idea behind the equation of continuity is that the rate of mass flow into the box must equal the time rate of change of the mass in the box (pur)l Figure 1: A small mathematical box in a fluid A) Consider just the 2-faces of the box for now. Figure 1 shows ρυ.Ε entering at and leaving at + ρ...
Given the velocity field u = xte1 + yte2 (where e1 and e2 are
unit vectors in the x and y direction, respectively) determine how
the density of the fluid varies with time. Assume the density is
independent of spatial position and that ρ = ρo at t = 0
I know that I need to substitute u into the equation of
continuity which is
ρo(∂s/∂t) + ∇*(ρo*û ) = 0 and solve for s but not
really sure how...
plz if you could make it clear.
will thumb up
5. (Hints: This derivation is presented in your textbook briefly. I also discussed that in the class. I would like you to provide step-by-step process for this mathematical derivation. You need to use the continuity equation (Eq. 6-21) for the derivation process) Starting from the first law of Thermodynamics for a differential control volume, derive the general governing equation for temperature (6-35) for a 2D flow over flat plate. Using...
Fluid Mechanics
Part 1 Correct The flo steady and you applied the continuity cquation co etty to this problem, first to compute the mass f ow rate at location 2 where all o the eriables are known, and then to determie te vel ty at ocation we er weigh t ls c a s t ough e nozzie that contracts from ธ diameter at IS cm to 2 cm, The exit speed is 2-3S m/s and at spheric pressure preve...
The rear suspension of a mountain bike consists of a spring suspended in a fluid and can be modelled as a spring and damper system. r(t) 1. Draw a free body diagram of the scenario above and show that the resulting ODE is given by dt m dt m where c is the damping constant, k is the spring stiffness, r(t) is the force pressing into the frame and r(t) is the downward displacement of the mass. 2. Find the...
Problem 7 (10 Pts) For the converging flow, write the continuity equation and show that V, = f(0)r. Then, write the r and components of the Navier-Stokes equations, and put the Vr into the r and 0 components of the Navier- Stokes equations. Lastly, write the no-slip boundary conditions using f(e). You do not need to solve the equations
Problem 7 (10 Pts) For the converging flow, write the continuity equation and show that V, = f(0)r. Then, write the...