A steady, incompressible, two-dimensional velocity field is given by the following components in the xy-plane: u = 1.85 + 2.33x + 0.656y, v = 0.754 - 2.18x - 2.33y. Calculate the acceleration field (find expressions for acceleration components a x and a y), and calculate the acceleration at the point (x, y) = (-1, 2).

A steady, incompressible, two-dimensional velocity field is given by $ec{V}=(u, v)=(1+2.5 x+y) ec{i}+(-0.5-3 x-2.5 y) ec{j}$where the x- and y-coordinates are in m and the magnitude of velocity is in m/s. (a) Determine if there are any stagnation points in this flow field, and if so, where they are. (b) Sketch velocity vectors at several locations in the upper- right quadrant for x = 0 m to 4 m and y= 0 m to 4 m; qualitatively describe the flow field.

A steady, incompressible, two-dimensional (in the xy-plane) velocity field is given by $ec{V}=(0.523-1.88 x+3.94 y) ec{i}+(-2.44+1.26 x+1.88 y) ec{j}$. Calculate the acceleration at the point (x, y) = (-1.55, 2.07).

A steady, incompressible, two-dimensional velocity field is given by $ec{V}=(u, v)=(2.5-1.6 x) ec{i}+(0.7+1.6 y) ec{j}$ where the x- and y-coordinates are in meters and the magnitude of velocity is in m/s. The shear strain rate in s–1 is(a) –1.6(b) 1.6(c) 2.5(d) 0.7(e) 0

A steady, incompressible, two-dimensional velocity field is given by the following components in the $x y$ plane:

$$\begin{aligned} &u=1.85+2.05 x+0.656 y \\ &v=0.754-2.18 x-2.05 y \end{aligned}$$

Determine the acceleration field (find expressions for acceleration components $a_x$ and $a_y$ ), and determine the acceleration at the point $(x, y)=(-1,3)$.

A steady, incompressible, two-dimensional velocity field is given by $ec{V}=(u, v)=(2.5-1.6 x) ec{i}+(0.7+1.6 y) ec{j}$ where the x- and y-coordinates are in meters and the magnitude of velocity is in m/s. The x- and y-component of material acceleration ax and ay at the point (x = 1 m, y = 1 m), respectively, in m/s2, are(a) –1.44, 3.68(b) –1.6, 1.5(c) 3.1, –1.32(d) 2.56, –4(e) –0.8, 1.6

Consider the steady, two-dimensional velocity field given by $ec{V}=(u, v)=(1.6+1.8 x) ec{i}+(1.5-1.8 y) ec{j}$. Verify that this flow field is incompressible.

A hair dryer is basically a duct of constant diameter in which a few layers of electric resistors are placed. A small fan pulls the air in and forces it through the resistors where it is heated. If the density of air is $1.20 ~\mathrm{\frac{kg}{m^3}}$ at the inlet and $0.95 ~\mathrm{\frac{kg}{m^3}}$ at the exit, determine the percent increase in the velocity of air as it flows through the dryer.

Explain why the friction factor is independent of the Reynolds number at very large Reynolds numbers.

Consider the following steady, incompressible, two- dimensional velocity field: $ec{V}=(u, v)=(4.35+0.656 x) ec{i}+(-1.22-0.656 y) ec{j}$. Generate an analytical expression for the flow streamlines and draw several streamlines in the upper-right quadrant from x = 0 to 5 and y= 0 to 6.

How does surface roughness affect the pressure drop in a pipe if the flow is turbulent? What would your response be if the flow were laminar?

Is the Lagrangian method of fluid flow analysis more similar to study of a system or a control volume? Explain.

What is the Eulerian description of fluid motion? How does it differ from the Lagrangian description?

A general equation for a steady, two-dimensional velocity field that is linear in both spatial directions (x and y) is $ec{V}=(u, v)=\left(U+a_{1} x+b_{1} y ight) ec{i}+\left(V+a_{2} x+b_{2} y ight) ec{j}$. Where U and V and the coefficients are constants. Their dimensions are assumed to be appropriately defined. Calculate the x- and y-components of the acceleration field.