Question

If the velocity distribution of a fluid flowing through a pipe is known, the flow rate Q (that is, the volume of water passing through the pipe per unit time) can be computed by $Q = \int vdA$ where $v$ is the velocity and $A$ is the pipe's cross-sectional area. (To grasp the meaning of this relationship physically, recall the close connection between summation and integration.) For a circular pipe, $A = \pi r^2$ and $dA = 2\pi rdr$. Therefore, $Q = \int_0^{r_0} v(2\pi r)dr$ where $r$ is the radial distance measured outward from the center of the pipe. If the velocity distribution is given by $v = 2(1 - \frac{r}{r_0})^{1/6}$ where $r_0$ is the total radius (in this case, 3 cm), compute Q using an appropriate built- in function of MATLAB.

          If the velocity distribution of a fluid flowing through a pipe is known, the flow rate Q
(that is, the volume of water passing through the pipe per unit time) can be computed
by $Q = \int vdA$ where $v$ is the velocity and $A$ is the pipe's cross-sectional area. (To grasp
the meaning of this relationship physically, recall the close connection between
summation and integration.) For a circular pipe, $A = \pi r^2$ and $dA = 2\pi rdr$. Therefore,
$Q = \int_0^{r_0} v(2\pi r)dr$
where $r$ is the radial distance measured outward from the center of the pipe. If the
velocity distribution is given by
$v = 2(1 - \frac{r}{r_0})^{1/6}$
where $r_0$ is the total radius (in this case, 3 cm), compute Q using an appropriate built-
in function of MATLAB.

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If the velocity distribution of a fluid flowing through a pipe is known, the flow rate Q
(that is, the volume of water passing through the pipe per unit time) can be computed
by Q = ∫ vdA where v is the velocity and A is the pipe's cross-sectional area. (To grasp
the meaning of this relationship physically, recall the close connection between
summation and integration.) For a circular pipe, A = π r^2 and dA = 2π rdr. Therefore,
Q = ∫0^r0 v(2π r)dr
where r is the radial distance measured outward from the center of the pipe. If the
velocity distribution is given by
v = 2(1 - (r)/(r0))^1/6
where r0 is the total radius (in this case, 3 cm), compute Q using an appropriate built-
in function of MATLAB.

Added by Jeremiah W.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Aman Kumar

Step 1

We are asked to compute the flow rate \(Q\), which is the volume of water passing through the pipe per unit time. The formula for \(Q\) involves integrating the velocity distribution across the cross-sectional area of the pipe. Show more…

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If the velocity distribution of a fluid flowing through a pipe is known, the flow rate Q (that is, the volume of water passing through the pipe per unit time) can be computed by Q=f vdA where v is the velocity and A is the pipe's cross-sectional area. (To grasp the meaning of this relationship physically, recall the close connection between summation and integration.) For a circular pipe, A = πr² and dA = 2πrdr. Therefore, Q = ["v(2nr)dr where r is the radial distance measured outward from the center of the pipe. If the velocity distribution is given by v = 2(1 - ¹/6 where ro is the total radius (in this case, 3 cm), compute Q using an appropriate built- in function of MATLAB. If the velocity distribution of a fluid flowing through a pipe is known,the flow rate Q (that is,the volume of water passing through the pipe per unit time) can be computed by Q= vdA where v is the velocity and A is the pipe's cross-sectional area.(To grasp the meaning of this relationship physically,recall the close connection between summation and integration.For a circular pipe,A=rand dA=2nrdr.Therefore, Q=v(2rr)dr where r is the radial distance measured outward from the center of the pipe.If the velocity distribution is given by v=2(1-5116 To where ro is the total radius(in this case,3 cm).compute Q using an appropriate built in function of MATLAB.

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