Lista halliday - fluidos

c05.qxd

10/29/07

1:18 PM

Page 316

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Chapter 5

Distributed Forces

Sample Problem 5/18
A rectangular plate, shown in vertical section AB, is 4 m high and 6 m wide (normal to the plane of the paper) and blocks the end of a fresh-water channel 3 m deep. The plate is hinged about a horizontal axis along its upper edge through A and is restrained from opening by the fixed ridge B which bears horizontally against the lower edge of the plate. Find the force B exerted on the plate by the ridge.
1m

A

3m B

Solution.

The free-body diagram of the plate is shown in section and includes the vertical and horizontal components of the force at A, the unspecified weight W mg of the plate, the unknown horizontal force B, and the resultant R of the triangular distribution of pressure against the vertical face. The density of fresh water is 1.000 Mg/m3 so that the average pressure is gh] pav 1.000(9.81)(2)
3

y Ay x Ax

[pav

14.72 kPa
2m R mg 4m

The resultant R of the pressure forces against the plate becomes [R pavA] R (14.72)(3)(6) 265 kN
1m B

This force acts through the centroid of the triangular distribution of pressure, which is 1 m above the bottom of the plate. A zero moment summation about A establishes the unknown force B. Thus, [ΣMA 0] 3(265) 4B 0 B 198.7 kN Ans.

Helpful Hint Note that the units of pressure gh are

103

kg m3

m (m) s2

103 kN/m2 kg m s2 kPa. 1 m2

Sample Problem 5/19
The air space in the closed fresh-water tank is maintained at a pressure of 5.5 kPa (above atmospheric). Determine the resultant force R exerted by the air and water on the end of the tank.
Air 500 mm A 160 mm

Water

600 mm

Solution.

The pressure distribution on the end surface is shown, where p0 5.5 kPa. The specific weight of fresh water is g 1000(9.81) 9.81 kN/m3 so that the increment of pressure p due to the water is p h 9.81(0.6) 5.89 kPa

Side view p0

B A

End view

The resultant forces R1 and R2