Pressure in Fluid Systems Sub Unit 1.2 – Fluid Force Pressure in Fluid Systems

Objectives Describe the four states of matter. Define density and pressure Explain why pressure in a fluid depends on depth in the fluid Explain why an object submerged in a fluid experiences a buoyant force Predict whether an object will sink or float in a given fluid. Explain how a force can be multiplied in a hydraulic lift. Explain where atmospheric pressure comes from. Describe how a barometer measures atmospheric pressure Explain the difference between absolute and gage pressure. Objectives

States of Matter Matter can exist in four states: Solid (ice) Liquid (water) Gas (steam vapor) Plasma (Extremely hot ionized atoms)

Fluids Fluids are materials that can flow, has no definite shape of its own, and conforms to the shape of its container. Liquids Gasses Fluid systems use both liquids (hydraulic) and gasses (pneumatic) to operate mechanical devices.

Hydraulic system under pressure City Water System Hydraulic system under pressure

Density and Pressure mass Density = volume m r = v Density is how much mass is contained in a given amount of space. Amount of matter per unit of volume. mass Density = (rho) volume m r = v

Units mass Density = volume (slugs) kg lb g or 3 3 ft 3 m cm English

Example The mass of 1 cm3 of water has a mass of 1g; therefore the density is 1g/1cm3.

Weight Density weight Weight Density = volume weight lb N r = 3 V ft 3 Weight Density is the comparison of an object’s weight to it’s volume weight Weight Density = volume weight lb N r = w 3 V ft 3 m Units

Weight Density of Water Water has a weight density of 62.4 lb/ft3.

Pressure force Pressure = area F lb N P = 2 2 A ft m A force applied over a surface is pressure. force Pressure = area Units F lb N P = 2 2 A ft m English SI

Pressure Units N/m2 = 1 Pascal (Pa) 1000 Pa = 1kilopascal (kPa) lb/in2 = psi (pounds per square inch)

Pressure and Depth Pressure = weight density x height P = r h x Pressure increase with depth because of the additional weight of the fluid above. Pressure = weight density x height P = r h x w

Buoyancy and Archimedes’ Principle Ptop = rw x h Pbottom = rw x (h + d) F = P x A Ftop = Ptop x A = (rw x h) x A Fbottom = Pbottom x A = [rw x (h+d)] x A Fbuoyant = Fbottom – Ftop = rw Ad Ad = Vbrick Fbuoyant = rw x Vbrick = weight of water displaced

Archimedes’ Principle An object immersed in a fluid has an upward force exerted on it equal to the weight of the fluid displaced by the object. Note: the buoyant force is based on the weight of the fluid displaced not on the weight of the object.

Pascal’s Principle A change in pressure at any point in a confined fluid is transmitted undiminished throughout the fluid. P = F / A or F = P x A A = p r2

Atmospheric Pressure The weight of the air above an area. At sea level, a column of air extending up through the atmosphere, with a cross sectional area of 1m2, encloses about 10,000 kg of air. This air weighs about 1 x 105 N Therefore, atmospheric pressure is about 105 Pa or 100kPa at sea level. Decreases with altitude This is why your ears pop (equalization)

Atmospheric Pressure Barometer – instrument used for measuring atmospheric pressure. At sea level the average atmospheric pressure is 101.3 kPa = 760mm of mercury = one atmosphere = 14.7 psi = 2117 lb/ft2

Absolute and Gage Pressure Absolute pressure is the total pressure measured above zero (perfect vacuum). Gage pressure is the pressure measured above atmospheric pressure. Absolute pressure = gage pressure + atmospheric pressure Suppose a tire gage measures the pressure of a tire to be 30 psi; Absolute pressure = 30 psi + 14.7 psi = 44.7 psi The air inside the tire pushes out with a pressure of 44.7 psi. The atmosphere pushes in with a pressure of 14.7 psi. The difference is 30 psi – the gage pressure.

Pressure is a Prime Mover Pressure acts like a force to cause movement.

Equilibrium

Summary Matter can exist in four states: solid, liquid, gas, and plasma. Liquids and gases are called fluids. The density of a substance is its mass per unit volume. The density of water is 1g/cm3. Weight density is weight per unit volume. Pressure is force divided by the area over which the force acts. We treat pressure as a scalar. In SI units, pressure is measured in pascals, where 1 Pa= 1 N/m Pressure increases with depth in a fluid.

Summary For a given fluid, the pressure does not depend on the size or shape of the container. When an object is submerged in a fluid, an upward force is exerted on the object caused by the pressure difference between the top and the bottom of the object. This force is called a buoyant force. The buoyant force exerted on a submerged object equals the weight of the fluid displaced by the object. A pressure applied to a confined fluid is transmitted throughout the fluid. Atmospheric pressure is caused by the weight of the air above a given area. Atmospheric pressure can be measured with a barometer. Absolute pressure is the sum of the gage pressure and atmospheric pressure.