Mechanical Properties of Fluids

Find the pressure at a depth of 10 m below the free surface of water. (Atmospheric pressure = 1.0 × 10⁵ Pa, density of water = 1000 kg/m³, g = 10 m/s²)

In a hydraulic lift, the input piston has an area of 5 cm² and the output piston has an area of 200 cm². If a force of 20 N is applied to the input piston, find the force exerted by the output piston.

A block of volume 2 × 10⁻³ m³ is fully submerged in water (density 1000 kg/m³). Find the buoyant force on it. (g = 10 m/s²)

A solid weighs 50 N in air and 30 N when fully immersed in water. Find its relative density.

A block of wood of density 600 kg/m³ floats in water of density 1000 kg/m³. What fraction of its volume remains above the water surface?

Water flows through a pipe of cross-sectional area 4 cm² with a speed of 2 m/s. It then enters a narrower section of area 1 cm². Find the speed of water in the narrower section.

Water flows horizontally through a pipe whose cross-section narrows so that the flow speed increases from 2 m/s to 4 m/s. Find the drop in pressure between the wide and narrow sections. (density of water = 1000 kg/m³)

A tank has water filled to a height of 5 m above a small hole near its base. Find the speed with which water emerges from the hole. (g = 10 m/s²)

A layer of liquid 2 mm thick is sheared between two plates, with the top plate moving at 0.5 m/s relative to the stationary bottom plate. If the coefficient of viscosity of the liquid is 1.2 Pa·s and the contact area is 0.02 m², find the viscous force required to maintain this motion.

A small sphere of radius 1 mm and density 2000 kg/m³ falls through a fluid of density 1000 kg/m³ and viscosity 0.5 Pa·s. Find its terminal velocity. (g = 10 m/s²)

Water flows through a pipe of diameter 2 cm with speed 1 m/s. Taking the density of water as 1000 kg/m³ and its viscosity as 1 × 10⁻³ Pa·s, find the Reynolds number and identify the type of flow.

Water flows through a horizontal capillary tube of radius 1 mm and length 0.2 m under a pressure difference of 1000 Pa. Taking the viscosity of water as 1 × 10⁻³ Pa·s, find the volume flow rate using Poiseuille's formula.

A wire ring of radius 2 cm is lifted out of a soap solution of surface tension 0.03 N/m. Ignoring the weight of the ring, find the additional force needed to pull it free of the liquid surface (the film clings to the ring on both its inner and outer edges).

Find the work done in forming a water drop of radius 1 mm, given the surface tension of water is 0.072 N/m.

Find the excess pressure inside a soap bubble of radius 1 cm, if the surface tension of the soap solution is 0.025 N/m.

Two soap bubbles of radii 3 cm and 4 cm coalesce in vacuum under isothermal conditions to form a single bubble. Find the radius of the resulting bubble.

Water rises to a height of 4 cm in a capillary tube of radius 0.5 mm. Find the surface tension of the liquid, given its density is 1000 kg/m³, angle of contact is 0°, and g = 10 m/s².

Water rises to a height of 6 cm in a capillary tube of radius r. If a second capillary tube of radius 2r is used instead (same liquid, same conditions), find the new height of rise.