A capillary tube of 1.2 mm diameter is immersed vertically in water exposed to the atmosphere. Determine how high water will rise in the tube. Take the contact angle at the inner wall of the tube to be $6^\circ$ and the surface tension to be 1.00 N/m.

The tube rests on a $1.5$-$\mathrm{mm}$ thin film of oil having a viscosity of $\mu=0.0586 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}^2$. If the tube is rotating at a constant angular velocity of $\omega=4.5\ \mathrm{rad} / \mathrm{s}$, find the torque $\mathbf{T}$ that must be applied to the tube to maintain the motion. Assume the velocity profile within the oil is linear.

For flow over a plate, the variation of velocity with vertical distance y from the plate is given as $u(y) = ay – by^2$ where a and b are constants. Obtain a relation for the wall shear stress in terms of a, b, and $\mu$.

A 2.4-in-diameter soap bubble is to be enlarged by blowing air into it. Taking the surface tension of soap solution to be 0.0027 lbf/ft, determine the work input required to inflate the bubble to a diameter of 2.7 in.

If a force of P=2N causes the $30$ -mm-diameter shaft to slide along the lubricated bearing with a constant speed of $0.5 \mathrm{~m} / \mathrm{s}$, determine the viscosity of the lubricant and the constant speed of the shaft when $P=8 \mathrm{~N}$. Assume the lubricant is a Newtonian fluid and the velocity profile between the shaft and the bearing is line ar. The gap between the bearing and the shaft is $1 \mathrm{~mm}$.

A 0.03-in-diameter glass tube is inserted into kerosene at $68^{\circ} \mathrm{F}.$ The contact angle of kerosene with a glass surface is $26^{\circ}.$ Determine the capillary rise of kerosene in the tube.

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).

In a steady, two-dimensional flow field in the xy - plane, the x-component of velocity is $u=a x+b y+c x^{2}$ where a, b, and c are constants with appropriate dimensions. Generate a general expression for velocity component v such that the flow field is incompressible.

Environmental scientists are increasingly concerned with the accumulation of toxic elements in marine mammals and the transfer of such elements to the animals' offspring. The striped dolphin (Stenella coeruleoalba), considered to be a top predator in the marine food chain, was the subject of one such study. The mercury concentrations (micrograms/gram) in the livers of 28 mals striped dolphins were as follows: 1.70 183.00 221.00 286.00 1.72 168.00 406.00 315.00 8.80 218.00 252.00 241.00 5.90 180.00 329.00 397.00 101.00 264.00 316.00 209.00 85.40 481.00 445.00 314.00 118.00 485.00 278.00 318.00 a. Calculate the five-number summary for the data. b. Construct a box plot for the data. c. Are there any outliers? d. If you knew that the first four dolphins were less than 3 years old, while all the others were more than 8 years old, would this information help explain the difference in the magnitude of those four observations? Explain.

A thin plate moves between two parallel, horizontal, stationary flat surfaces at a constant velocity of $5 \mathrm{~m} / \mathrm{s}$. The two stationary surfaces are spaced $4 \mathrm{~cm}$ apart, and the medium between them is filled with oil whose viscosity is $0.9 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}^2$. The part of the plate immersed in oil at any given time is $2$-$\mathrm{m}$ long and $0.5$-$\mathrm{m}$ wide. If the plate moves through the mid-plane between the surfaces, find the force required to maintain this motion. What would your response be if the plate was $1 \mathrm{~cm}$ from the bottom surface $\left(h_2\right)$ and $3 \mathrm{~cm}$ from the top surface $\left(h_1\right)$ ?

The tube rests on a $1.5$-$\mathrm{mm}$ thin film of oil having a viscosity of $\mu=0.0586 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}^2$. If the tube is rotating at a constant angular velocity of $\omega=4.5\ \mathrm{rad} / \mathrm{s}$, find the shear stress in the oil at $r=40 \mathrm{~mm}$ and $r=80 \mathrm{~mm}$. Assume the velocity profile within the oil is linear.

The viscosity of a fluid is to be measured by a viscometer constructed of two $75$-$\mathrm{cm}$-long concentric cylinders. The outer diameter of the inner cylinder is $15 \mathrm{~cm}$, and the gap between the two cylinders is $1 \mathrm{~mm}$. The inner cylinder is rotated at $300\ \mathrm{rpm}$, and the torque is measured to be $0.8 \mathrm{~N} \cdot \mathrm{m}$. Find the viscosity of the fluid.

A fluid that occupies a volume of 24 L weighs 225 N at a location where the gravitational acceleration is $9.80 m/s^2.$ Determine the mass of this fluid and its density.

If the kinematic viscosity of glycerin is $v=1.15\left(10^{-3}\right) \mathrm{m}^2 / \mathrm{s}$, find its viscosity in FPS units. At the temperature considered, glycerin's specific gravity is $S_g=1.26$