Mechanical properties of fluids practice · Mixed difficulty

A fully loaded Boeing aircraft 747 has a mass of $33 \times 10^5 \mathrm{~kg}$. Its total wing area is $500 \mathrm{~m}^2$. It is in level flight with a speed of $960 \mathrm{~km} / \mathrm{h}$. (a) Estimate the pressure difference between the lower and upper surfaces of the wings. (b) Estimate the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface. The density of air is $\rho=1.2 \mathrm{~kg} \mathrm{~m}^{-3}$ and $g=9.81 \mathrm{~ms}^{-2}$.

A liquid drop of radius $r$ and surface tension $T$ is split into 125 drops of equal size work done in this process is

A horizontal pipe of cross-sectional diameter 4 cm carries water at a speed of 6 m/s. The pipe is connected to a smaller pipe with a cross-sectional diameter 2 cm. The velocity of the water through the smaller pipe is

The lift of an air plane is based on

Two copper vessels $A$ and $B$ have the same
base area but of different shapes. $A$ take twice
the volume of water as that $B$ requires to fill
upto a particular common height. Then the
correct statement among the following is:

A vessel, whose boom has round holes with a diameter of 0.1mm, is filled with water. The maximum height to which the water can be filled without leakage is (S.T. of water =$75\mathrm{ }dyne/cm,\mathrm{ }g\mathrm{ } = 1000\mathrm{ }cm/{s^2}$)

Assertion(A): The water rises higher in a capillary tube of small diameter than in the capillary tube of large diameter.

Reason(R): Height through which liquid rise in capillary tube inversely proportional to the diameter of capillary tube.

A manometer connected to a close tap reads $3.5 \times {10^5}\mathrm{N}{\mathrm{m}^{ - 2}}$. When the valve is opened, the reading of manometer falls to $3.0 \times {10^5}\mathrm{N}{\mathrm{m}^{ - 2}}$ , then velocity of flow of water is

A: Needle placed carefully on the surface of water may float, where as a ball of same material sinks
R: Archimedes principle is applicable for only spherical bodies

A: According to Archimede's principle when body is floating the weight of liquid displaced by body is equal to the weight of the body
R: A man is sitting in a boat which is floating on a pond. If the man drinks some water from the pond, the level of the water in the pond decreases

Pressure applied to an enclosed fluid is transmitted undiminished to every point of the fluid and the walls of containing vessel. This law was first formulated by:

A soap bubble of radius $R$, surface tension $T$ exists in equilibrium in vacuum. A monoatomic gas is trapped inside the soap bubble. Charge $\mathrm{Q}$ is given to bubble such that bubble expands from radius a to radius $2 \mathrm{a}$ under reversible adiabatic condition. If surface charge density on the bubble surface is found to be $\sqrt{\frac{x \varepsilon_0 T}{y a}}$. Find the value of $x / y .(x, y$ are positive co-primes)

A piece of gold $\left(\rho=19.3 \mathrm{~g} / \mathrm{cm}^3\right)$ has a cavity in it. It weights $38.2 \mathrm{~g}$ in air and $36.2 \mathrm{~g}$ in water. The volume of the cavity in gold is

When a pinch of salt or any other salt which is soluble in water is added to water, its surface tension

A small spherical ball of steel falls through a viscous medium with terminal velocity $v$. If a ball of twice the radius of the first one but of the same mass is dropped through the same method, it will fall with a terminal velocity (neglect buoyancy)

Statement A: Water flows faster than honey.
Statement B: The coefficient of viscosity of water is less than honey.

With the increase in temperature, the angle of contact

The velocity of kerosene oil in a horizontal
pipe is $5 \, \text{ms}^{-1}.$ If $g=10 \, \text{ms}^{-2},$ then the velocity
head of oil will be

Density of ice is $\rho$ and that of water is $\sigma$. What will be the decrease in volume when a mass $M$ of ice melts

A fluid flows through a horizontal pipe having two different cross-sections of area $A$ and$2A$. If the pressure at the thin cross-section is $p$and fluid velocity is $v$, the velocity and pressure at the thicker cross-section is (take the density of fluid as $\rho$)

A raindrop with radius $1.5mm$ falls from a cloud at a height $1200\mathrm{m}$ from ground. The density of water is $1000kg/{m^3}$and density of air is $1.2kg/{m^3}$. Assume the drop was spherical throughout the fall and there is no air drag. The impact speed of the drop will be

Work done in forming a soap bubble of radius ${R}$ is ${W}$ then work done in forming a soap bubble of radius $2 {R}$ will be:

A: Machine parts are jammed in winter.
R: The viscosity of lubricant used in machine parts increase at low temperature.

In Millikan's oil drop experiment, what is the terminal speed of a drop of radius $2.0 \times 10^{-5} \mathrm{~m}$ and density $1.2 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$? Take the viscosity of air at the temperature of the experiment to be $1.8 \times 10^{-5} \mathrm{~Nsm}^{-2}$. How much is the viscous force on the drop at that speed? Neglect buoyancy of the drop due to air.

A capillary tube of radius $r$ can support a liquid of weight $6.28 \times 10^{-4} \mathrm{~N}$. If the surface tension of the liquid is $2 \times 10^{-2} \mathrm{~N} / \mathrm{m}$ then find:

(1) Radius of capillary tube.

(2) Internal circumference of capillary tube.

Two spherical bubbles are in contact with each other internally as shown. The radius of curvature of the common surface is R, then -

Two capillary of length L and 2L and of radii R and 2R are connected in series. The net rate of flow of fluid through them will be (given rate of the flow through single capillary, X= $\frac{{\pi p{R^4}}}{{8\eta L}}$)

The level of water in a tank is $5 \mathrm{~m}$ high. A hole of area $1 \mathrm{~cm}^2$ is made at the bottom of the tank. The rate of leakage of water from the hole is (Take, $g=10 \mathrm{~ms}^{-2}$ )

Spherical ball of radius $R$ are falling in a viscous fluid of viscosity ɳ with a velocity $v$. The retarding viscous force acting on the spherical ball is

A: The blood pressure in human is greater at the feet than at the brain
R: Pressure of liquid at any point is proportional to height, density of liquid and acceleration due to gravity