# Fluid Mechanics Lesson 3

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Problem 1 Problem 1

A vertical rectangular gate 1.5 m wide and 3

A vertical rectangular gate 1.5 m wide and 3 m high is submerged in m high is submerged in water with its top edge 2 m bewater with its top edge 2 m be low the water surface. Findlow the water surface. Find the total pressure acting on one side of the gate and its location from the bottom.

the total pressure acting on one side of the gate and its location from the bottom. Ans; 154.51 kN; 1.286 m

Ans; 154.51 kN; 1.286 m Problem 2

Problem 2

A vertical triangular gate with top

A vertical triangular gate with top base horizontal and 1.5 wide is 3 m high. It base horizontal and 1.5 wide is 3 m high. It is submerged in oil having sp. is submerged in oil having sp. gr. Of 0.82 with itsgr. Of 0.82 with its top base submerged to a depth of

top base submerged to a depth of 2 m. determine the magnitude and location 2 m. determine the magnitude and location of the total hydrostatic of the total hydrostatic pressure acting on onepressure acting on one side of the gate.

side of the gate.

Ans; 54.30 kN; 3.1667 m Ans; 54.30 kN; 3.1667 m Problem 3

Problem 3

A vertical rectangular plate is submerged

A vertical rectangular plate is submerged half in oil (sp. gr.=0.8) and half in water half in oil (sp. gr.=0.8) and half in water such that its top edge isuch that its top edge i s flushed with the oils flushed with the oil surface. What is the ratio of the force exerted by water acting on the lower half to that by oil acting on the upper half? surface. What is the ratio of the force exerted by water acting on the lower half to that by oil acting on the upper half? Ans; 3.25

Ans; 3.25 Problem 4 Problem 4

A vertical circular gate in a

A vertical circular gate in a tunnel 8 m diameter has oil (sp. gtunnel 8 m diameter has oil (sp. g r. 0.8) on one side and air on tr. 0.8) on one side and air on t he other side. If oil is 12 he other side. If oil is 12 m above them above the invert and the air pressure is 40

invert and the air pressure is 40 kPa, where will a single support be lockPa, where will a single support be loc ated (above the invert of the tunnel) to ated (above the invert of the tunnel) to hold the gate inhold the gate in position? position? Ans; Ans; Problem 6 Problem 6

A closed cylindrical tank 2 m in diameter and 8 m deep with axis vertical contains 6 m deep of oil (sp. gr.

A closed cylindrical tank 2 m in diameter and 8 m deep with axis vertical contains 6 m deep of oil (sp. gr. = 0.8). The air above= 0.8). The air above the liquid surface has a pressure of

the liquid surface has a pressure of 0.8 kg/cm0.8 kg/cm22. Determine the total normal force in kg acting on the wall at its location from the. Determine the total normal force in kg acting on the wall at its location from the

bottom of the tank. bottom of the tank.

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Determine the magnitude and location of the total hydrostatic force acting on the 2 m x 4 m gate shown in the figure.

Problem 8

The crest gate shown consists of a c ylindrical surface of which AB is the base supported by a structural f rame hinged at O. the length of the gate is 10 m. compute the magnitude and location of the horizontal and vertical components of the total pressure on AB.

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In the figure shown, the 1.20 m diameter cylinder. 1.20 m long is acted upon by water on the left and oil having sp. gr. Of 0.80 on the right. Determine the components of the reaction at B if the cylinder weighs 19.62 kN.

Problem 10

The section of a gravity dam is as shown in the figure. Assume hydrostatic uplift to vary uniformly from full hydrostatic uplift from the heel to zero at the toe. determine the total reaction per unit length at the base of the dam. Use sp. gr. Of concrete =2.4

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The section of the masonry dam is as shown. The specific weight of water is 9.81 kN/m3 and that of co ncrete is 23.54 kN/m3.

Assuming uplift pressure varies linearly from maximum hydrostatic pressure at the heel to zero at the location of t he drain, determine the (a.) location of the resultant force, (b) factor of safety against sliding if coefficient of friction is 0.75, (c) factor of safety against overturning, (d) the stress at heel and at the toe, and (e) the unit horizontal shearing stress at the base.

Problem 12

An iceberg having specific gravity of 0.92 is floating on salt water o f sp. gr. 1.03. if the volume of ice above the water surface is 1000 cu. m., what is the total volume of the ice?

Problem 13

A block of wood 0.60 m x 0.60 m x h meters in dimension was thrown into the water and floats with 0.18 m projecting above the water surface. The same block was thrown into a container of a liquid having a sp. gr. Of 0.90 and it floats with 0.14 m projecting above the surface. Determine the following:

a.) The value of h

b.) The sp. gr. Of the block c.) The weight of the block Problem 14

Determine the magnitude of the f orce on the inclined gate 1.5 m by 0.5 m shown in the figure. The tank o f water is completely closed and the pressure gage at the bottom of the tank reads 90,000 N/m2. Use 9800 N/m3 for water.

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Calculate the magnitude of the resultant force per meter length due to water acting on the radial tainter gate shown in the figure.

Problem 16

Determine the magnitude of the horizontal and vertical components of the total force per meter length acting on the three-quarter cylinder gate shown.

References

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