If an incompressible liquid is flowing through a horizontal pipe having branches of area A, 0.4 A, and 0.5 A as shown in the figure, then the value of v is:
                               

The continuity equation for fluid flow is based on the principle of the

Blood flows in an artery of radius R in a Laminar manner under pressure p with a flow rate Q. If the radius gets halved and the pressure quadruples, the new rate of flow will be

Two water droplets merge with each other to form a larger droplet isothermally. In this process

 From the given diagram, the velocity ${\mathrm{v}}_3$ is:
                        

The value of Reynold's number for which the flow of water through a pipe becomes turbulent is:

The diameter of a syringe is 4 mm and the diameter of its nozzle (opening) is 1 mm. The syringe is placed on the table horizontally at a height of 1.25 m. If the piston is moved at a speed of 0.5 m/s, then considering the liquid in the syringe to be ideal, the horizontal range of liquid is-

(g = 10 m/${\mathrm{s}}^2$)

A lead sphere of mass m falls in a viscous liquid with terminal velocity v. Another lead sphere of mass M falls through the liquid with terminal velocity 4v. The ratio M/m is:

For amongst the following curves which one shows the variation of velocity with time for a small-sized spherical body falling vertically in a long column of viscous liquids

A sphere of mass m is dropped from a tall tower when it falls by 10 m, it attains terminal velocity and continues to fall at that speed. The work done by air friction against the sphere during the first 10 m is ${\mathrm{w}}_1$ and during next 10 m is ${\mathrm{w}}_2$ then

Water is flowing from a source as shown in the figure. Let A be the cross-sectional area of the liquid flow at the time when velocity is 5 m/s. The cross-sectional area of the liquid flow when the water has descended by 10 meters is [Take g = 10 m/${\mathrm{s}}^2$]

Two equal drops of water are falling through air with a steady velocity v. If the drops coalesce, the new steady velocity will be

A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is :

In a horizontal pipe of non-uniform cross-section, water flows with a velocity of 1 m s${}^{-1}$ at a point where the diameter of the pipe is 20 cm. The velocity of water (m s${}^{-1}$) at a point where the diameter of the pipe is 5 cm is-

A liquid does not wet the solid surface if the angle of contact is :

A barometer is constructed using a liquid (density = 760 kg/${\mathrm{m}}^3$). What would be the height of the liquid column, when a mercury barometer reads 76 cm? (density of mercury = 13600 kg/${\mathrm{m}}^3$)

Bernoulli's theorem is applicable in the case of:

In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are 70 m s^–1and 63 m s^-1 respectively. What is the lift on the wing if its area is 2.5 m²? (Take the density of air to be 1.3 kg m^–3.)

$$\begin{gathered} \left(1\right) 2.5\times {10}^5 N \\ \left(2\right) 1.5\times {10}^5 N \\ \left(3\right) 2.5\times {10}^3 N \\ \left(4\right) 1.5\times {10}^3 N \end{gathered}$$

The cylindrical tube of a spray pump has a cross-section of 8.0 cm² one end of which has 40 fine holes each of diameter 1.0 mm. If the liquid flow inside the tube is 1.5 m min^–1,  the speed of ejection of the liquid through the holes is:

$$\begin{gathered} \left(1\right) 0.64 m{s}^{-1} \\ \left(2\right) 0.74 m{s}^{-1} \\ \left(3\right) 0.54 m{s}^{-1} \\ \left(4\right) 0.84 m{s}^{-1} \end{gathered}$$

A U-shaped wire is dipped in a soap solution and removed. The thin soap film formed between the wire and the light slider supports a weight of 1.5 × 10^–2 N (which includes the small weight of the slider). The length of the slider is 30 cm. The surface tension of the film is:

$$\begin{gathered} \left(1\right) 3.5\times {10}^{-2} N m^{-1} \\ \left(2\right) 2.5\times {10}^{-2} N m^{-1} \\ \left(3\right) 3.5\times {10}^{-3} N m^{-1} \\ \left(4\right) 2.5\times {10}^{-3} N m^{-1} \end{gathered}$$

What is the pressure inside the drop of mercury of radius 3.00 mm at room temperature? The surface tension of mercury at that temperature (${20}^0 C$) is 4.65 × 10^–1 N m^–1. The atmospheric pressure is 1.01 × 10⁵ Pa.

$$\begin{gathered} \left(1\right) 2.30\times {10}^5 Pa \\ \left(2\right) 2.01\times {10}^{5 }Pa \\ \left(3\right) 3.01\times {10}^5 Pa \\ \left(4\right) 1.01\times {10}^5 Pa \end{gathered}$$

The blades of a windmill sweep out a circle of area A. If the wind flows at a velocity v perpendicular to the circle, what is the mass of the air passing through it in time t?

$$\begin{gathered} 1. \mathrm{\rho Avt} \\ 2. \frac{1}{2}\mathrm{\rho Avt} \\ 3. 2 \mathrm{\rho Avt} \\ 4. \frac{3}{2} \mathrm{\rho Avt} \end{gathered}$$

Which one of the following is true from the given statements?

What is the largest average velocity of blood flowing in an artery of radius 2×10^–3 m if the flow must remain laminar?

(Take viscosity of blood to be 2.084 × 10^–3 Pa-sec and density of blood to be 1.06 × 10³ kg/m³).

A tall cylinder is filled with viscous oil. A round pebble is dropped from the top with zero initial velocity. From the plot shown in the figure, indicate the one that represents the velocity(v) of the pebble as a function of time (t).

A 50 kg girl wearing high heel shoes balances on a single heel. The heel is circular with a diameter of 1.0 cm. What is the pressure exerted by the heel on the horizontal floor?

$$\begin{gathered} \left(1\right) 6.24\times {10}^6 N m^{-2} \\ \left(2\right) 4.21\times {10}^5 N m^{-2} \\ \left(3\right) 3.20\times {10}^6 N m^{-2} \\ \left(4\right) 1.01\times {10}^5 N m^{-2} \end{gathered}$$

Toricelli’s barometer used mercury. Pascal duplicated it using French wine of density $.$ The height of the wine column for normal atmospheric pressure is:

A hydraulic automobile lift is designed to lift cars with a maximum mass of 3000 kg. The area of cross-section of the piston carrying the load is 425 cm². What maximum pressure would the smaller piston have to bear?

$$\begin{gathered} \left(1\right) 3.12\times {10}^5 Pa \\ \left(2\right) 1.01\times {10}^5 Pa \\ \left(3\right) 2.94\times {10}^5 Pa \\ \left(4\right) 6.92\times {10}^5 Pa \end{gathered}$$

A U-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with 10.0 cm of water in one arm and 12.5 cm of spirit in the other. What is the specific gravity of the spirit?

Glycerine flows steadily through a horizontal tube of a length of 1.5 m and a radius of 1.0 cm. If the amount of glycerine collected per second at one end is 4.0 × 10^–3 kg s^–1, what is the pressure difference between the two ends of the tube?

$$\begin{gathered} \left(1\right) 7.9\times {10}^{-2} Pa \\ \left(2\right) 8.9\times {10}^{-3} Pa \\ \left(3\right) 9.8\times {10}^{-2} Pa \\ \left(4\right) 6.7\times {10}^{-3} Pa \end{gathered}$$

(Density of glycerine = $1.3\times {10}^3$ kg m^–3 and viscosity of glycerine = 0.83 Pa-sec).