Mechanical Prop...

The velocity of efflux is:

A cylindrical vessel of cross-sectional area $$1000 cm^2$$, is fitted with a frictionless piston of mass $$10 kg$$, and filled with water completely. A small hole of cross-sectional area $$10 mm^2$$ is opened at a point $$50 cm$$ deep from the lower surface of the piston. The velocity of efflux from the hole will be

Find the speed with which water comes out of the hole.

Find the height of the water in the long tube above the top when the water stops coming out of the hole.

Find the height $$h_2$$ of the water in the long tube above the top initially.

A cubical box of wine has a small spout located in one of the bottom corners. When the box is full and placed on a level surface, opening the spout results in a flow of wine with an initial speed of $${ v }_{ 0 }$$ (see figure). When the  box is half empty, someone tilts it at $${ 45 }^{ \circ  }$$ so that the spout is at the lowest point (see figure). When the spout is opened the wine will flow out with a speed of

Figure shows a capillary tube of radius $$r$$ dipped into water. If the atmospheric pressure is $$P_0$$, the pressure at point $$A$$ ( just below the meniscus ) is

Air is streaming past a horizontal airplane wing such that its speed is $$90 ms^{-1}$$ at the lower surface and $$120 ms^{-1}$$ over the upper surface. If the wing is 10 m long and has an average width of 2m, the difference of pressure on the two sides and the gross lift on the wing respectively, are (density of air $$=1.3 kg m^{-3})$$

The initial speed of efflux without cylinder is:

What work should be done in order to squeeze all water from a horizontally located cylinder (figure shown above) during the time $$t$$ by means of a constant force acting on the piston? The volume of water in the cylinder is equal to $$V$$, the cross-sectional area of the orifice to $$s$$, with $$s$$ being considerably less than the piston area. The friction and viscosity are negligibly small.