The airplane wing is a beautiful example of Bernoulli's principle in action.
[link] (a) shows the characteristic shape of a wing. The wing is tilted upward at a small angle and the upper surface is longer, causing air to flow faster over it. The pressure on top of the wing is therefore reduced, creating a net upward force or lift. (Wings can also gain lift by pushing air downward, utilizing the conservation of momentum principle. The deflected air molecules result in an upward force on the wing — Newton's third law.) Sails also have the characteristic shape of a wing. (See
[link] (b).) The pressure on the front side of the sail,
, is lower than the pressure on the back of the sail,
. This results in a forward force and even allows you to sail into the wind.
Making connections: take-home investigation with two strips of paper
For a good illustration of Bernoulli's principle, make two strips of paper, each about 15 cm long and 4 cm wide. Hold the small end of one strip up to your lips and let it drape over your finger. Blow across the paper. What happens? Now hold two strips of paper up to your lips, separated by your fingers. Blow between the strips. What happens?
Velocity measurement
[link] shows two devices that measure fluid velocity based on Bernoulli's principle. The manometer in
[link] (a) is connected to two tubes that are small enough not to appreciably disturb the flow. The tube facing the oncoming fluid creates a dead spot having zero velocity (
) in front of it, while fluid passing the other tube has velocity
. This means that Bernoulli's principle as stated in
becomes
Thus pressure
over the second opening is reduced by
, and so the fluid in the manometer rises by
on the side connected to the second opening, where
(Recall that the symbol
means “proportional to.”) Solving for
, we see that
[link] (b) shows a version of this device that is in common use for measuring various fluid velocities; such devices are frequently used as air speed indicators in aircraft.
Summary
Bernoulli's equation states that the sum on each side of the following equation is constant, or the same at any two points in an incompressible frictionless fluid:
Bernoulli's principle is Bernoulli's equation applied to situations in which depth is constant. The terms involving depth (or height
h ) subtract out, yielding
Bernoulli's principle has many applications, including entrainment, wings and sails, and velocity measurement.
Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ...
Step 2: Find each score's deviation from the mean. ...
Step 3: Square each deviation from the mean. ...
Step 4: Find the sum of squares. ...
Step 5: Divide the sum of squares by n – 1 or N.
The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.
Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400
a. what is the probability of getting more than 12,000 hits?
b. what is the probability of getting fewer than 9,000 hits?
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400.
a. What is the probability of getting more than 12,000 hits