Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

(II)A fish tank has dimensions 36 cm wide by 1.0 m long by 0.60 m high. If the filter should process all the water in the tank once every 3.0 h, what should the flow speed be in the 3.0 cm diameter input tube for the filter?

Short Answer

Expert verified

The flow speed in input tube for the filter is \(0.028\;{\rm{m/s}}\).

Step by step solution

01

Understanding the concept of volume flow rate

The volume flow rate shows the amount of fluid flow through a specific area in a certain period, and it is calculated by the product of the area and velocity of a fluid.

02

Given data

The width of fish tank is \(b = 36\;{\rm{cm}}\).

The length of fish tank is \(l = 1.0\;{\rm{m}}\).

The height of fish tank is \(h = 0.60\;{\rm{m}}\).

The time taken by filter to process all water is \(\Delta t = 3.0\;{\rm{h}}\).

The diameter of input tube for the filter is \(d = 3.0\;{\rm{cm}}\).

03

Evaluating the flow speed in input tube by using volume flow rate

The flow speed in input tube for the filter is calculated below:

\(\begin{array}{c}\frac{V}{{\Delta t}} = Av\\v = \frac{V}{{A\Delta t}}\\v = \frac{{b \times h \times l}}{{\left( {\frac{\pi }{4}{d^2}} \right)\Delta t}}\end{array}\)

Here, A is the area and V is the volume.

Substitute the values in the above equation.

\(\begin{array}{c}v = \frac{{\left( {36\;{\rm{cm}} \times \frac{{1\;{\rm{m}}}}{{100\;{\rm{cm}}}}} \right) \times \left( {0.60\;{\rm{m}}} \right) \times \left( {1.0\;{\rm{m}}} \right)}}{{\left[ {\frac{\pi }{4}{{\left( {3.0\;{\rm{cm}} \times \frac{{1\;{\rm{m}}}}{{100\;{\rm{cm}}}}} \right)}^2}} \right]\left( {3.0\;{\rm{h}} \times \frac{{3600\;{\rm{s}}}}{{1\;{\rm{h}}}}} \right)}}\\v = 0.028\;{\rm{m/s}}\end{array}\)

Hence, the flow speed in input tube for the filter is \(0.028\;{\rm{m/s}}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Two ships moving in parallel paths close to one another risk colliding. Why?

Intravenous transfusions are often made under gravity, as shown in Fig. 10–55. Assuming the fluid has a density of \({\bf{1}}{\bf{.00\;g/c}}{{\bf{m}}^{\bf{3}}}\)at what height h should the bottle be placed so the liquid pressure is (a) 52 mm-Hg, and (b) \({\bf{680\;mm - }}{{\bf{H}}_{\bf{2}}}{\bf{O?}}\)(c) If the blood pressure is 75 mm-Hg above atmospheric pressure, how high should the bottle be placed so that the fluid just barely enters the vein?

(II) If the base of an insect’s leg has a radius of about \(3.0 \times 1{0^{{\bf{ - }}5}}\;m\) and the insect’s mass is 0.016 g, would you expect the six-legged insect to remain on top of the water? Why or why not?

(II) Poiseuille’s equation does not hold if the flow velocity is high enough that turbulence sets in. The onset of turbulence occurs when the Reynolds number, \(Re\) , exceeds approximately 2000. \(Re\) is defined as

\({\mathop{\rm Re}\nolimits} = \frac{{2\overline v r\rho }}{\eta }\)

where \(\overline v \) is the average speed of the fluid, \(\rho \) is its density, \(\eta \) is its viscosity, and \(r\) is the radius of the tube in which the fluid is flowing. (a) Determine if blood flow through the aorta is laminar or turbulent when the average speed of blood in the aorta \(\left( {{\bf{r = 0}}{\bf{.80}}\;{\bf{cm}}} \right)\) during the resting part of the heart’s cycle is about \({\bf{35}}\;{\bf{cm/s}}\). (b) During exercise, the blood-flow speed approximately doubles. Calculate the Reynolds number in this case, and determine if the flow is laminar or turbulent.

A 3.2-N force is applied to the plunger of a hypodermic needle. If the diameter of the plunger is 1.3 cm and that of the needle is 0.20 mm, (a) with what force does the fluid leave the needle? (b) What force on the plunger would be needed to push fluid into a vein where the gauge pressure is 75 mm-Hg? Answer for the instant just before the fluid starts to move.

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free