Fluid Mechanics Lesson 3

Module 3; Fluids and Hydraulics Problem 1

A vertical rectangular gate 1.5 m wide and 3 m high is submerged in water with its top edge 2 m be low the water surface. Find the total pressure acting on one side of the gate and its location from the bottom. Ans; 154.51 kN; 1.286 m Problem 2

A vertical triangular gate with top base horizontal and 1.5 wide is 3 m high. It is submerged in oil having sp. gr. Of 0.82 with its top base submerged to a depth of 2 m. determine the magnitude and location of the total hydrostatic pressure acting on one side of the gate. Ans; 54.30 kN; 3.1667 m Problem 3

A vertical rectangular plate is submerged half in oil (sp. gr.=0.8) and half in water such that its top edge i s 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? Ans; 3.25 Problem 4

A vertical circular gate in a tunnel 8 m diameter has oil (sp. g r. 0.8) on one side and air on t he other side. If oil is 12 m above the invert and the air pressure is 40 kPa, where will a single support be loc ated (above the invert of the tunnel) to hold the gate in position? Ans;

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. = 0.8). The air above the liquid surface has a pressure of 0.8 kg/cm2. Determine the total normal force in kg acting on the wall at its location from the bottom of the tank.

Problem 7

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.

Problem 9

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

Problem 11 (dam)

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.

Problem 15

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 threequarter cylinder gate shown.