### Shortcut Methods

**Shortcuts and Tricks for Solving Numericals on Mechanical Properties of Fluids**

**1. Density and Specific Gravity:**

- To find the density of a substance, divide its mass by its volume.
- To find the specific gravity of a substance, divide its density by the density of water at 4°C (1000 kg/m³).

**2. Pressure:**

- Pressure is directly proportional to the force applied and inversely proportional to the area over which the force is applied.
- The pressure exerted by a liquid at a given depth is equal to the product of the density of the liquid, the acceleration due to gravity, and the depth.

**3. Buoyancy:**

- The buoyant force acting on an object is equal to the weight of the fluid displaced by the object.
- The density of an object can be determined by finding the ratio of its weight in air to its weight in water.

**4. Viscosity:**

- The force required to move an object through a fluid is directly proportional to the coefficient of viscosity of the fluid, the velocity of the object, and the surface area of the object.
- The Reynolds number is a dimensionless quantity that characterizes the flow of a fluid and is used to determine whether the flow is laminar or turbulent.

**5. Surface Tension:**

- The surface tension of a liquid is the force per unit length acting on the surface of the liquid.
- The excess pressure inside a soap bubble is equal to twice the surface tension of the soap solution divided by the radius of the bubble.