396
9 Fluid Dynamics
Fig. 9.4
the cylinder, s being much smaller than the cross-sectional area of the piston
(Fig. 9.5). Show that the work to be done by a constant force acting on the
piston to squeeze all water from the cylinder in time t is given by
W =
1
2
ρV 3
s 2 t 2
where ρ is the density of water. Neglect friction and viscosity.
Fig. 9.5
9.15 A cylindrical vessel with water is rotated about its vertical axis with a constant
angular velocity ω. Show that
(a) the water pressure distribution along its radius is given by P = P 0 +
1
2 ρω 2 r 2 , where ρ is the density of water and P 0 is the pressure at the
central point.
(b) Show that the figure of revolution of water is a paraboloid.
9.16 A manometer is fixed to a water tap. When the valve is closed the manometer
shows the reading of 3.5×10 5 Pa. When the valve is open the reading becomes
3.1 × 10 5 Pa. Find the speed of water.
9.2.2 Torricelli’s Theorem
9.17 A water container is filled up to a height H . A small hole is punched at the
side wall at a depth h below the water surface. Show (a) that the distance from
the foot of the wall at which the stream strikes the floor is 2
√
h(H − h); (b)
the second hole through which the second stream has the same range must be
punched at a depth H − h.
9 Fluid Dynamics
Fig. 9.4
the cylinder, s being much smaller than the cross-sectional area of the piston
(Fig. 9.5). Show that the work to be done by a constant force acting on the
piston to squeeze all water from the cylinder in time t is given by
W =
1
2
ρV 3
s 2 t 2
where ρ is the density of water. Neglect friction and viscosity.
Fig. 9.5
9.15 A cylindrical vessel with water is rotated about its vertical axis with a constant
angular velocity ω. Show that
(a) the water pressure distribution along its radius is given by P = P 0 +
1
2 ρω 2 r 2 , where ρ is the density of water and P 0 is the pressure at the
central point.
(b) Show that the figure of revolution of water is a paraboloid.
9.16 A manometer is fixed to a water tap. When the valve is closed the manometer
shows the reading of 3.5×10 5 Pa. When the valve is open the reading becomes
3.1 × 10 5 Pa. Find the speed of water.
9.2.2 Torricelli’s Theorem
9.17 A water container is filled up to a height H . A small hole is punched at the
side wall at a depth h below the water surface. Show (a) that the distance from
the foot of the wall at which the stream strikes the floor is 2
√
h(H − h); (b)
the second hole through which the second stream has the same range must be
punched at a depth H − h.