The marine water strider, Halobates, has a mass of $0.36 \mathrm{~g}$. If it has six slender legs, find the minimum contact length of all of its legs combined to support itself in water having a temperature of $T=20^{\circ} \mathrm{C}$. Take $\sigma=72.7\ \mathrm{mN} / \mathrm{m}$, and assume the legs are thin cylinders that are water repellent.

The marine water strider, Halobates, has a mass of $0.36 \mathrm{~g}$. If it has six slender legs, find the minimum contact length of all of its legs combined to keep itself in water having a temperature of $T=20^{\circ} \mathrm{C}$. Assume $\sigma=72.7 \mathrm{mN} / \mathrm{m}$, and suppose the legs to be thin cylinders with a contact angle of $\theta=0^{\circ}$.

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 $1 \mathrm{~mm}$.

Fossil fuels are commonly used as an energy source for transportation vehicles. Burning fossil fuels has led to more carbon dioxide in the atmosphere and dissolved in seawater. Which of the following describes how burning fossil fuels is MOST LIKELY to impact marine organisms? A. Increased levels of carbon dioxide in seawater would increase the rate of photosynthesis in marine plants. B. Dissolved carbon dioxide in seawater would cause an increase in shellfish populations due to strengthened skeletons. C. Increased levels of carbon dioxide in seawater would cause ocean acidification and weaken corals. D. Dissolved carbon dioxide in seawater would cause invasive species to out-compete native species.

Compare and evaluate the adaptations of multicellular organisms, such as sponges, and unicellular organisms for obtaining food.

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 $S_g=1.26$

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.

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 $\left(h_1\right)$ ?

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 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 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 degree and the surface tension to be 1.00 N / m.

Water at $25^{\circ} \mathrm{C}$ is flowing through a garden hose. If the hose is bent, a hissing noise can be heard. Here cavitation has occurred in the hose because the velocity of the flow has increased at the bend, and the pressure has dropped. What would be the highest absolute pressure in the hose at this location in the hose?

A $50-cm imes 30-cm imes 20-cm$ block weighing 150 N is to be moved at a constant velocity of 0.80 m/s on an inclined surface with a friction coefficient of 0.27. (a) Determine the force F that needs to be applied in the horizontal direction. (b) If a 0.40-mm-thick oil film with a dynamic viscosity of $0.012 Pa\cdot s$ is applied between the block and inclined surface, determine the percent reduction in the required force.

The Newtonian fluid is confined between the plate and a fixed surface. If its velocity profile is defined by $u=\left(8 y-0.3 y^2\right) \mathrm{mm} / \mathrm{s}$, where $y$ is in $\mathrm{mm}$, find the force $\mathbf{P}$ that must be applied to the plate to cause this motion. The plate has a surface area of $15\left(10^3\right) \mathrm{mm}^2$ in contact with the fluid. Assume $\mu=0.482 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}^2$.