Fluid
mechanics
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This document covers a brief overview of fluid mechanics.
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2019/2020
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Fluid
mechanics
Fluid Mechanics
- A fluid is a collection of molecules that are
randomly arranged and held together by weak cohesive
forces and by forces exerted by the walls of a
container.
- It is any substance that does not have a definite
shape and exhibits the phenomenon of flow
- It includes LIQUIDS and GASES.
Example
Your grandmother gave you a gold ring as “pamana”.
The gold ring is 5.00 mm thick and has an outside
diameter of 12.00 mm and an inside diameter of
11.00 mm. The density of gold is 1.93 x 10
4
kg/m
3
◍ What is its volume in cubic millimeters?
◍ What is its mass in grams?
◍ What is its current market value if the price of
gold is P1836.15 per gram?
Pressure
Pressure is force per unit area. The unit of pressure is Pascal
(Pa).
𝐹 𝐴
The Pressure P at depth h in a liquid is given by: P = P 0 + pgh
◍ Here, P 0 is the pressure at the surface
◍ P is the fluid’s density
◍ g is the acceleration due to gravity
Pascal’s principle
- States that pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel.
1 𝐴 1 =
2 𝐴 2
Example
As you are passing by a car repair shop, you
notice that a car is being lifted in a hydraulic
automobile lift.
- What must be the ratio of the diameter of the vessel at the car to the diameter of the vessel where the force F 1 is applied so that a 1200-kg car can be lifted with a force F 1 of just 120 N?
- The piston of the hydraulic automobile lift is 0.5 m in diameter. What gauge pressure, in pascals, is required to lift a car with a mass of 1200 kg?
- What is the pressure of the atmosphere?
Example A plastic spherical balloon is held below the surface of a swimming pool by a cable tied to the bottom of the pool. The sphere has a volume of 1.50 x 10
- 2 m 3 and the tension in the cable is 90.0 N a. What is the buoyant force exerted by the water on the sphere? b. Calculate the mass of the balloon. c. A swimmer breaks the cable and the balloon rises to the surface. What fraction of its volume will be submerged when the balloon comes to rest?
Continuity Equation Ideal fluids exhibit the following characteristics:
- non-turbulent flows
- steady-state flow
- non-viscous
- incompressible. For a fluid flowing through a pipe, the volume flow rate 𝑑𝑉 𝑑𝑡
is constant as given by Av (i.e.
𝑑𝑉 𝑑𝑡
= Av), where A is the
cross-sectional are and v is the flow speed.
In a varying cross-sectional area, the continuity equation is given by: 𝐴 1 𝑣 1 = 𝐴 2 𝑣 2
Bernoulli’s Equation
This equation relates pressure, flow velocity,
and height for flow of an ideal fluid.
P_1+1/2 pv_1^2+pgy_1=P_2+1/2 pv_2^2+pgy_
When a moving fluid enters a narrower
section of pipe, its speed increases but the
pressure on the fluid decreases.
Example A small circular hole 5.00 mm in diameter is cut in the side of a large water tank, 11.0 m below water level in the tank. The water tank is sealed and contains air above the water at a gauge pressure of 2.00 atm.