03 Water flowing into rectangular trough

Problem 03
A rectangular trough is 10 ft long and 3 ft wide. Find how fast the surface rises, if water flows in at the rate of 12 ft3/min.
 

01-02 Water flowing into cylindrical tank

Problem 01
Water is flowing into a vertical cylindrical tank at the rate of 24 ft3/min. If the radius of the tank is 4 ft, how fast is the surface rising?
 

Problem 02
Water flows into a vertical cylindrical tank at 12 ft3/min, the surface rises 6 in/min. Find the radius of the tank.
 

Solution to Problem 674 | Midspan Deflection

Problem 674
Find the deflection midway between the supports for the overhanging beam shown in Fig. P-674.
 

Overhang beam with point load at the free end

 

Solution to Problem 673 | Midspan Deflection

Problem 673
For the beam shown in Fig. P-673, show that the midspan deflection is δ = (Pb/48EI) (3L2 - 4b2).
 

Simple beam with concentrated load

 

Midspan Deflection | Deflections in Simply Supported Beams

In simply supported beams, the tangent drawn to the elastic curve at the point of maximum deflection is horizontal and parallel to the unloaded beam. It simply means that the deviation from unsettling supports to the horizontal tangent is equal to the maximum deflection. If the simple beam is symmetrically loaded, the maximum deflection will occur at the midspan.
 

Spherical Wedge and Spherical Lune

A spherical wedge is a solid formed by revolving a semi-circle about its diameter by less than 360°. Spherical Lune is the curve surface of the wedge, it is a surface formed by revolving a semi-circular arc about its diameter by less than 360°.
 

Spherical Sector

A spherical sector is a solid generated by revolving a sector of a circle about an axis which passes through the center of the circle but which contains no point inside the sector. If the axis of revolution is one of the radial sides, the sector thus formed is spherical cone; otherwise, it is open spherical sector.
 

Open Spherical Sector and Spherical Cone

 

Spherical Segment

Four Powerful Ways of Solving the Volume of Frustum of a Sphere

Spherical segment is a solid bounded by two parallel planes through a sphere. In terms of spherical zone, spherical segment is a solid bounded by a zone and the planes of a zone's bases.
 

Spherical segment of two bases

 

Spherical Zone

Zone
A zone is that portion of the surface of the sphere included between two parallel planes.
 

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