(a) Express this pressure in the following units. INEED CORRECT CLEAR SOLUTION P
ID: 2077697 • Letter: #
Question
(a) Express this pressure in the following units.
INEED CORRECT CLEAR SOLUTION PLEASE
P = Pa P = atm P= mm HgThe tank in the figure below is filled with water of depth d = 2.70 m. At the bottom of one sidewall is a rectangular hatch of height h = 1.20 m and width w = 1.90 m that is hinged at the top of the hatch. (a) Determine the magnitude of the force the water exerts on the hatch. kN (b) Find the magnitude of the torque exerted by the water about the hinges. kN middot m The human brain and spinal cord are immersed in the cerebrospinal fluid. The fluid is normally continuous between the cranial and spinal cavities and exerts a pressure of 100 to 200 mm of H_2O above the prevailing atmospheric pressure. In medical work, pressures are often measured in units of mm of H_2O because body fluids, including the cerebrospinal fluid, typically have the same density as water. The pressure of the cerebrospinal fluid can be measured by means of a spinal tap as Illustrated in the figure below. A hollow tube Is inserted into the spinal column, and the height to which the fluid rises Is observed. If the fluid rises to a height of 163 mm, we write its gauge pressure as 163 mm H_2O.
Explanation / Answer
consider, at distance x from the bottom of the container
for depth, dx
Area of the hatch , dA = wdx
Hydrostatic pressure, P = rho*g*(d - x)
so force, dF = PdA = rho*g(d-x)wdx
a) Net force = rho*g(d-x)wdx { from x = 0 to x = h} = rho*g*w(dh - h^2/2)
rho = 1000
w = 1.9 m
d = 2.7 m
h = 1.2 m
F = 46970.28 N
b) Net moment = rho*g(d-x)(h - x)wdx { from x = 0 to x = h} = rho*g(dh - dx - xh + x^2)wdx = rho*g(d - h/3)wh^2/2 = 30866.184 Nm
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