Q = flow rate at every cross section (water is incompressible for our purposes) = v A = 4.50 m/s * 0.080 m^2 = 0.36 m^3/s
so
answer part b first
0.36 m^3/s * 500 hr * 3600 s/hr = 648,000 m^3 in 500 hours (heavens to Betsy, what a waste ! )
now part a
4.50 * ( .08/.101) = 3.56 m/s
Water is flowing in a pipe with a circular cross-section area, and at all points
the water completely fills the pipe. At point 1, the cross-section area of the
pipe is 0.080-m2 and the fluid velocity is 4.50 m/s.
(a) What is the fluid speed at a point in the pipe where the cross-sectional area
is 0.101 m2?
(b) Calculate the volume of the water discharge from the open end of the pine
in 500 hours.
5 answers
a mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror the pipe is located 8 inches from the vertex of the mirror write an equation of the parabola that models the cross section of the mirror assume that the parabola opens upward
Let's assume that the parabola has its vertex at the origin, with the axis of symmetry along the y-axis. Then, the equation of the parabola is of the form y = ax^2, where a is a constant that determines the shape of the parabola.
To find the value of a, we need to use the information given about the mirror and the pipe. We know that the pipe is located at the focus of the mirror, which is a point on the axis of symmetry. We also know that the pipe is 8 inches from the vertex of the mirror, which means it is located at a distance of 8 inches along the y-axis.
The distance between the vertex and the focus of a parabola is given by the constant a/4. In this case, we have a distance of 8 inches, so we can write:
a/4 = 8
Solving for a, we find:
a = 32
Therefore, the equation of the parabola that models the cross section of the mirror is:
y = 32x^2
To find the value of a, we need to use the information given about the mirror and the pipe. We know that the pipe is located at the focus of the mirror, which is a point on the axis of symmetry. We also know that the pipe is 8 inches from the vertex of the mirror, which means it is located at a distance of 8 inches along the y-axis.
The distance between the vertex and the focus of a parabola is given by the constant a/4. In this case, we have a distance of 8 inches, so we can write:
a/4 = 8
Solving for a, we find:
a = 32
Therefore, the equation of the parabola that models the cross section of the mirror is:
y = 32x^2
a mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror the pipe is located 8 inches from the vertex of the mirror write an equation of the parabola that models the cross section of the mirror assume that the parabola opens upward
A. y=1/48x^2
B. y=1/64x^2
C. y=1/16x^2
D. y=1/32x^2
A. y=1/48x^2
B. y=1/64x^2
C. y=1/16x^2
D. y=1/32x^2
The correct answer is D. y = 1/32x^2.
We can start by using the formula for a parabolic mirror, which is given by:
y = a*x^2 / (4*f)
where y is the vertical axis, x is the horizontal axis, a is the curvature of the mirror, and f is the focal length.
In this problem, we are given that the pipe is located at the focus of the mirror, which means that f = 8 inches. We are also told that the mirror has a parabolic cross section that opens upward, so a > 0.
To find the value of a, we can use the fact that the distance from the vertex of the parabola (the point where the slope is zero) to the focus is equal to f/2. In this problem, the vertex is located at the origin, so we can write:
a = 4*f / d^2
where d is the distance from the vertex to the pipe. In this case, d = 8 inches, so we have:
a = 4*8 / 8^2 = 1/2
Substituting this value of a and f = 8 into the equation for a parabolic mirror, we get:
y = (1/2)*x^2 / (4*8) = 1/64 * x^2
Therefore, the equation of the parabola that models the cross section of the mirror is:
y = 1/64x^2
So the answer is B, which is different from the answer I gave earlier. I apologize for the mistake in my previous response.
We can start by using the formula for a parabolic mirror, which is given by:
y = a*x^2 / (4*f)
where y is the vertical axis, x is the horizontal axis, a is the curvature of the mirror, and f is the focal length.
In this problem, we are given that the pipe is located at the focus of the mirror, which means that f = 8 inches. We are also told that the mirror has a parabolic cross section that opens upward, so a > 0.
To find the value of a, we can use the fact that the distance from the vertex of the parabola (the point where the slope is zero) to the focus is equal to f/2. In this problem, the vertex is located at the origin, so we can write:
a = 4*f / d^2
where d is the distance from the vertex to the pipe. In this case, d = 8 inches, so we have:
a = 4*8 / 8^2 = 1/2
Substituting this value of a and f = 8 into the equation for a parabolic mirror, we get:
y = (1/2)*x^2 / (4*8) = 1/64 * x^2
Therefore, the equation of the parabola that models the cross section of the mirror is:
y = 1/64x^2
So the answer is B, which is different from the answer I gave earlier. I apologize for the mistake in my previous response.
1 answer