Solved Problems

Applying fluid property formulas to practical scenarios.

Example

Problem 1: A reservoir of oil has a mass of 825 kg. The reservoir has a volume of 0.917 m³. Calculate the density, specific weight, and specific gravity of the oil.

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Example

Problem 2: A flat plate of area 1.5 m² is pulled with a speed of 0.4 m/s relative to another stationary plate located at a distance of 0.15 mm from it. Find the force and power required to maintain this speed, if the fluid separating them is castor oil with a dynamic viscosity \mu = 0.981 \text{ Pa}\cdot\text{s}.

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Example

Problem 3: Calculate the capillary rise in a glass tube of 2.5 mm diameter when immersed vertically in (a) water and (b) mercury. Take surface tensions \sigma = 0.0725 \text{ N/m} for water and \sigma = 0.52 \text{ N/m} for mercury. The contact angle for mercury is 130°. Assume the contact angle for water is 0°.

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Example

Problem 4: Compressibility and Bulk Modulus A liquid is compressed in a cylinder. It has a volume of 1000 cm31000 \text{ cm}^3 at 1 MPa1 \text{ MPa} and a volume of 995 cm3995 \text{ cm}^3 at 2 MPa2 \text{ MPa}. Calculate its bulk modulus of elasticity.

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Example

Problem 5: Ideal Gas Law Calculate the density of air at a pressure of 150 kPa150 \text{ kPa} (absolute) and a temperature of 30C30^\circ\text{C}. Use the gas constant for air R=287 J/(kgK)R = 287 \text{ J/(kg}\cdot\text{K)}.

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Case Study 1: Non-Newtonian Fluids in Engineering

Context: In civil engineering, understanding fluid behavior goes beyond water and air. Many materials used in construction and encountered in nature are non-Newtonian fluids.
Application: Concrete pumping is a classic example. Fresh concrete behaves as a Bingham plastic—it requires a certain yield stress to be overcome before it starts flowing. Once flowing, its apparent viscosity decreases. This property is crucial for designing pump systems and ensuring concrete can be transported to high elevations without segregating. Similarly, drilling muds used in geotechnical engineering exhibit shear-thinning behavior, allowing them to flow easily when pumped but gel when stationary to suspend cuttings.

Case Study 2: Surface Tension in Soil Mechanics

Context: Capillary action driven by surface tension plays a significant role in geotechnical and agricultural engineering.
Application: In fine-grained soils like silts and clays, the small void spaces act as capillary tubes. Surface tension draws water upward above the water table, creating a capillary fringe. This phenomenon can cause soils to remain saturated even above the water table, affecting the soil's effective stress and shear strength. In cold climates, capillary action can lead to frost heave, where water is drawn into freezing zones, forming ice lenses that lift and damage pavements and light structures.