3. Understanding of Convective and Diffusive Fluxes. A solution containing species A in water moves to the right with a mass average velocity of 0.06cm/min. Species A obeys Fick's law with diffusion coefficient of 10-5 cm²/s. The mass concentration of species A vs. position is shown in the figure. Find the diffusion flux of species A at the position x=2cm. Is the total flux of A greater or less than the convective flux of A? Justify your answer. PA (g/ml) 0.004- Flow 0.003 0.002 0.001 0 0 1 2 3 x (cm)

9. WATER DRAINING FROM A BOTTLE When water flows out of a bottle, the potential energy of the water (Ep = mgh = pAh, where p is the density of water, A is the cross-sectional area of the bottle and h is the height of the water in the bottle) is turned into kinetic energy (Ek = mv² = pa(d)2, where a is the cross-sectional area of the hole out of which the water drains). Energy is conserved, so these quantities must be equal: Ek = Ep 1 dh pa()² = pAh dt we can simplify this equation to (dh)² = dt = 2=h a Let's define the ratio A/a as the constant c, which we could measure. Then, taking the square root of both sides, we get the equation dh √2ch dt where we negative sign arises because we know the height of the water in the bottle decreases with time. a.) Solve the differential equation for h(t) assuming the initial height is h(0) = 1. Don't worry about units, and your answer will involve the known constant c. b.) Of course, the height of water in the bucket should decrease and,…

27a) drop down box option is (stable, unstable)

(.) If a mass of 7 kg stretches a spring 3 cm beyond its natural length, what is the spring constant k?

8-16a)

To investigate the fluid mechanics of swimming, twenty swimmers each swam a specified distance in a water-filled pool and in a pool where the water was thickened with food grade guar gum to create a syrup-like consistency. Velocity, in meters per second, was recorded and the results are given in the table below. Velocity (m/s) Swimmer Water Guar Syrup 1 0.90 0.93 0.92 0.98 3 1.00 0.95 4 1.10 1.14 1.20 1.23 6. 1.25 1.23 7 1.25 1.28 1.30 1.30 9 1.35 1.31 10 1.40 1.42 11 1.40 1.41 12 1.50 1.53 13 1.65 1.59 14 1.70 1.70 15 1.75 1.80 16 1.80 1.78

To investigate the fluid mechanics of swimming, twenty swimmers each swam a specified distance in a water-filled pool and in a pool where the water was thickened with food grade guar gum to create a syrup-like consistency. Velocity, in meters per second, was recorded and the results are given in the table below. Velocity (m/s) Swimmer Ho: Md=0 Ha: Hd <0 1 O Ho: Md <0 H₂Hd = 0 2 o Ho Hoto H₂Hd = 0 3 4 5 6 7 8 9 10 11 12 o Ho Mozo H:H 0 13 14 15 16 17 18 19 20 Water Guar Syrup 0.90 0.92 1.00 1.10 1.20 1.25 1.25 1.30 1.35 1.40 1.40 1.50 1.65 1.70 1.75 1.80 1.80 1.85 1.90 1.95 0.93 0.97 0.95 1.14 1.23 1.23 1.27 1.30 1.34 1.42 1.44 1.53 1.59 1.70 1.80 1.77 1.84 The researchers concluded that swimming in guar syrup does not change mean swimming speed. Are the given data consistent with this conclusion? Carry out a hypothesis test using a 0.01 significance level. (Use μ = μwater-guar syrup) 1.86 State the appropriate null and alternative hypotheses. O Ho: Md = 0 H₂:μg 0 1.89 1.95 Find the…

The capacity of a certain filtering equipment is defined as the volume of the filtrate (Vt) per total time per run. The total time of run is tf + tw + tc where t is the total time per run t = tę is the filtration time tw is the washing time, normally 1/5 of tf te is the assembling and dismantling time, constant at 7 hrs per run The volume of the filtrate (V;) is a function of tf, is given by: V; = 150 /tf + 0.15 Find the maximum capacity of the filtering equipment with respect to the filtration time tr.

Consider the temperature distribution in a 2 ×1 rectangular plate as described in the figure below. Determine the steady-state temperature distribution u (x, y) in the plate. Calculate the steady-sate temperature at the centre of the plate. Ice at 0°-. 1 Ice at 0° Ice at 0° 2 Boiling water at 100°

2. Height of a rocket If an external force F acts upon a system whose mass varies with time, Newton's law of motion is d(mv) dm - = F + (v + u) dt dt In this equation, m is the mass of the system at time t, v is its velocity, and v + u is the velocity of the mass that is entering (or leaving) the system at the rate dm/dt. Suppose that a rocket of initial mass mo starts from rest, but is driven upward by fir- ing some of its mass directly backward at the constant rate of dm/dt = -b units per second and at constant speed relative to the rocket u =-c. The only external force acting on the rocket is F = -mg due to gravity. Under these assumptions, show that the height of the rocket above the ground at the end of t seconds (t small compared to mo/b) is то — bt, mo — bt In - žer. y = тo