Chapter 11 – Forces in Fluids

Pressure The amount of pressure you exert depends on the area over which you exert force. Pressure is equal to the force exerted on a surface divided by the total area over which the force is exerted.

Unbalanced Pressure

Formula, Variables, & Units Formula: Pressure = Force / Area Variables: Pressure = P Force = F Area = a Units: 1 n / m 2 or 1 Pa

Pressure Problem If a baseball strikes a mitt with a force of 200 N over an area of m 2, what is the pressure?

Solution P = F / a 200 N / m 2 = 66,667 Pa

Independent Practice Problems 1.What is the pressure applied by a piston that has an area of 15 cm 2 and exerts a force of 40 N ? 2.A 1.8 kg mass measure 8 cm in width, 12 cm in length and 6 cm in height. It is resting on a wooden floor. What pressure does it exert on the floor?

Solutions 1.P = F / a = 40 N /.15 m 2 = 267 Pa 2.First solve for area: a = l x w = 8 x 12 = 96 cm 2 or.96 m 2 Then solve for force: F = ma = 1.8 kg x 9.8 m / s 2 = 17.6 N Finally solve for pressure: P = F / a = 17.6 N /.96 m 2 = 18.3 Pa

Fluid Pressure A fluid is a material that can easily flow. As a result, a fluid can change shape. In a fluid, all of the forces exerted by the individual particles combine to make up the pressure exerted by the fluid. Atmospheric pressure decreases as your elevation increases. Water pressure increases as depth increases. You can measure atmospheric pressure with an instrument called a barometer.

Density Density of a substance is its mass per unit of volume. Formula: Density = Mass / Volume Variables : Density = D Mass = M Volume = V Units: g / cm 3

Density Sample Problems 1. Suppose that a metal object has a mass of 57 grams and a volume of 21 cm 3. Calculate its density. 2. A sample of liquid has a mass of 24 grams and a volume of 16 milliliters. What is its density?

Sample Problems Solutions 1. D = M / V = 57 g / 21 cm 3 = 2.7 g / cm 3 2. D = M / V = 24 g / 16 ml = 1.5 g / ml

Independent Problems 1. A piece of metal has a density of 2.9 g / cm 3 and a mass of 43.5 grams. What is its volume? 2. A fluid that is in a container with equal sides of 18 cm has a density of 2.8 g / cm 3. What is the fluids mass?

Solutions 1. D = M / V solve for volume V = M / D = 43.5 grams / 2.9 g / cm 3 = 15 cm 3 2. D = M / V, first solve for volume: v = l x w x h = 5832 cm 3 solve for mass M = D x V = 2.8 g / cm 3 x 5832 cm 3 = 16,330 g

More Density Info. By comparing densities, you can predict whether an object will float or sink in a fluid. Density > 1 then object will sink Density < 1 then object will float Density = 1 then object floats at a constant depth.

Density Column

Buoyancy Water and other fluids exert an upward force called the buoyant force that acts on a submerged object. The buoyant force acts in the direction opposite to the force of gravity, so it makes an object feel lighter. The less dense the object is, the greater the buoyant force it experiences.

Buoyant Force and Weight

Archimedes Principle Archimedes principle states that the buoyant force acting on a submerged object is equal to the weight of the volume of fluid displaced by the object Submarines – changing the water level in the floatation tanks changes the weight of the submarine and allows it to rise or sink. Balloons – a balloon filled with air is denser than the surrounding air because the air inside it is under pressure. The denser air makes it fall to the ground. If heated the balloon rises.

Buoyant Force Sample Problems 1. If an object that floats on the surface displaces 30 cm 3 of water, how much does that object weigh? 2. An object weighing 560 N floats on a lake. What is the weight of the displaced water? What is the buoyant force?

Solutions 1. Since the object floats, it is equal to the amount of water that is displaced. This would mean that the object weighs 30 N. 2. Because the object floats, the weight of the displaced water equals the weight of the object, 560 N. The buoyant force on the object equals its weight, 560 N.

Pascal’s Principle Pascal’s principle states that the pressure increases by the same amount throughout an enclosed or confined fluid. When force is applied to a confined fluid, the change in pressure is transmitted equally to all parts of the fluid. A hydraulic system uses liquids to transmit pressure and multiply force in a confined fluid.

Pascal’s Principle Continued A hydraulic system multiplies force by applying the force to a small surface area. The increase in pressure is then transmitted to another part of the confined fluid, which pushes on a larger surface area.

Hydraulic Devices

Pascal’s Principle Sample Problem 1. Suppose you apply a 50 N force to a 20 cm 2 piston in a hydraulic device. If the force is transmitted to another piston that is 200 cm 2, by how much will the force be multiplied?

Solution The force will be multiplied ten times because the surface area of the larger piston is ten times greater. Therefore, the larger piston will apply a force of 500 N.

Hydraulic Brakes

Bernoulli’s Principle A fluid tends to flow from an area of high pressure to an area of low pressure. Bernoulli’s principle states that the faster a fluid moves, the less pressure the fluid exerts. Bernoulli’s principle states that as the speed of a moving fluid increase, the pressure exerted by the fluid decreases.

Bernoulli’s Principle Continued Bernoulli’s principle helps explain how planes fly. It also helps explain how an atomizer works, why smoke rises up a chimney, and how a flying disk glides through the air.