Consider steady, incompressible, axisymmetric flow (r, z) and (ur, uz) for which the stream function is defined as ur = −(1/r)(∂?/∂z) and uz = (1/r)(∂?/∂r). Verify that ? so defined satisfies the continuity equation. What conditions or restrictions are required on ??

3.3 The velocity field of a flow is given by V = x²tj + (xt - 2xyt) j a) Determine whether it is steady or unsteady, one, two or three dimensional flow b) Is it an incompressible flow? c) Is it an irrotational flow? d) Determine the equation of streamline passing through the point (x,y)= (1,0).

It’s a fluid mechanics

choose the correct answer     Q1A- the major formula in hardy-cross method is Darcy-weisbach equation *       a) True       b) False                  B- The vertical intercept between E.G.L and H.G.L is equal to *       a) pressure head       b) potential head       c) kinetic head       d) Piezometric head       E)none of all above

8 the velocity components for a certain flow field are Vx=-3/2y and Vy=x. comment on its steadiness and space dimensionality. is the flow rotational

7. Stream function of the 2D flow is given as Y =x² + y² a. Find the velocity components for each direction b. Determine stream lines equations. c. Find the flow has velocity potential or not. d. Determine the velocity potential function if its possible.

Question

Q1- : Water flows out of a lake into steep slope wide rectangular channel (n = 0.017) as shown below. The flow enters the channel at depth = h = 1.15m. Water surface hc= 1.15m Lake Channel So Downstream the lake, select a logical value for the flow depth (h) along the channel reach. So = 0.012 Based on all selected values, compute the distance (Ax) downstream the lake such that the flow depth = selected h value.

Consider the general form of the Reynolds transport theorem (RTT) given by dBsys / dt = d/dt ∫CV ρb dV +∫CS ρbV-›r·n-› dAwhere V-›r is the velocity of the fluid relative to the control surface. . Let Bsys be the angular momentum H-› = r→ × mV-› of a system of fluid particles, where r → is the moment arm. We know that for a system, conservation of angular momentum is                                                                                   ∑M-›= d / dt   H-›sys                                                                   where Σ M-› is the net moment applied to the system. Use the RTT and the above equation to derive the equation of conservation of angular momentum for a control volume.

4. For a steady, incompressible two-dimensional flow, represented in Cartesian co- ordinates (x, y), a student correctly writes the equation of pathline of any arbitrary dx = ax and • by, dt particle as, 'dt where a and b are constants having unit of (second)'. If value of a is 5, determine the value of b.