Consider a 0.15-mm diameter air bubble in a liquid. Determine the pressure difference between the inside and outside of the air bubble if the surface tension at the air-liquid interface is (a) 0.080 N/m and (b) 0.12 N/m.

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 $1 \mathrm{~mm}$.

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.

Consider a 0.15 -mm-diameter air bubble in a liquid. Determine the pressure difference between the inside and outside of the air bubble if the surface tension at the air-liquid interface is

(a) 0.080 N / m and

(b) 0.12 N / m.

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.

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.

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 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 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 $S_g=1.26$

A 1.2-mm-diameter tube is inserted into an unknown liquid whose density is $960 kg/m^3$, and it is observed that the liquid rises 5 mm in the tube, making a contact angle of $15^\circ$. Determine the surface tension of the liquid.

A 1.2-mm-diameter tube is inserted into an unknown liquid whose density is $960 kg/m^3,$ and it is observed that the liquid rises 5 mm in the tube, making a contact angle of $15^\circ.$ Determine the surface tension of the liquid.

The density of seawater at a free surface where the pressure is 98 kPa is approximately $1030 kg/m^3.$ Taking the bulk modulus of elasticity of seawater to be $2.34 imes 109 N/m^2$ and expressing variation of pressure with depth as $dP= ho g\ dz$ determine the density and pressure at a depth of 2500 m. Disregard the effect of temperature.

Calculate the pressure difference between the inside and outside of a spherical water droplet having a diameter of $\frac{1}{32}$ in. and a temperature of 50 $^{\circ} \mathrm{F}$.

A large plate is pulled at a constant speed of $U=$ $4 \mathrm{~m} / \mathrm{s}$ over a fixed plate on $5$-mm-thick engine oil film at $20^{\circ} \mathrm{C}$. Assuming a half-parabolic velocity profile in the oil film, while the flow is developing as sketched, find the shear stress on the upper plate and its direction. Repeat for the linear profile (dashed line) that develops after a long time.