/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 91 \( \mathrm{A}\) smooth, 75 -mm-d... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 91

\( \mathrm{A}\) smooth, 75 -mm-diameter pipe carries water \(\left(65^{\circ} \mathrm{C}\right)\) horizontally. When the mass flow rate is \(0.075 \mathrm{kg} / \mathrm{s}\), the pressure drop is measured to be 7.5 Pa per \(100 \mathrm{m}\) of pipe. Based on these measurements, what is the friction factor? What is the Reynolds number? Does this Reynolds number generally indicate laminar or turbulent flow? Is the flow actually laminar or turbulent?

Short Answer

Expert verified
The calculated Reynolds number indicates whether the flow is laminar or turbulent. Then, based on the Reynolds number and the known data, the friction factor is calculated. Depending on the Reynolds number result, the flow is either laminar or turbulent.

Step by step solution

01

Calculate velocity

First, let's calculate the velocity of the water in the pipe. The formula for this is \( v = \frac{4m}{{\pi d^2}} \) where 'm' is the mass flow rate (0.075 kg/s), and 'd' is the diameter of the pipe (75 mm or 0.075 m).
02

Calculate kinematic viscosity

Next, the kinematic viscosity of water at 65掳 C needs to be determined. You could refer to a fluid properties table, or use a calculator that computes dynamic fluid properties. For this example, the kinematic viscosity is 0.000000281 m虏/s.
03

Calculate Reynolds number

The Reynolds number is a dimensionless quantity that helps indicate whether a flow is laminar or turbulent. It is given by \( R = \frac{4m}{\pi d \nu} \) where '\( \nu \)' is the kinematic viscosity determined from Step 2. If the Reynolds number is less than 2,000, the flow is considered to be laminar. If it's greater than 4,000, it is considered to be turbulent. Anything in between is transitional flow.
04

Verify if the flow is Laminar or Turbulent

After calculating the Reynolds Number, compare it with the standard values to determine whether the flow is laminar, turbulent or in transition.
05

Calculate friction factor

Finally, we will compute the friction factor using the formula \( f = \frac{{\Delta p d}}{2 \rho L v^2} \) where '\( \Delta p \)' is the measured pressure drop (7.5 Pa/100m or 0.075 Pa/m), 'd' is the diameter of the pipe (0.075 m), 'L' is the length of the pipe (per unit 1 m length), '\(v\)' is the velocity calculated in Step 1, and '\(\rho\)' is the density of water at 65掳C (which can again be referred to from fluid properties table or a calculator, for this case, we will take it as 983 kg/m鲁).

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 91影视!

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

Water discharges to atmosphere from a large reservoir through a moderately rounded horizontal nozzle of \(25 \mathrm{mm}\) diameter. The free surface is \(2.5 \mathrm{m}\) above the nozzle exit plane. Calculate the change in thow rate when a short section of 50 -mm-diameter pipe is attached to the end of the nozzle to form a sudden expansion. Determine the location and estimate the magnitude of the minimum pressure with the sudden expansion in place. If the flow were frictionless (with the sudden expansion in place), would the minimum pressure be higher, lower, or the same? Would the flow rate be higher, lower, or the same?

A continuous belt, passing upward through a chemical bath at speed \(U_{0},\) picks up a liquid film of thickness \(h,\) density \(\rho,\) and viscosity \(\mu .\) Gravity tends to make the liquid drain down, but the movement of the belt keeps the liquid from running off completely. Assume that the flow is fully developed and laminar with zero pressure gradicnt, and that the atmosphere produces no shear stress at the outer surface of the film. State clearly the boundary conditions to be satisfied by the velocity at \(y=0\) and \(y=h\). Obtain an expression for the velocity profile.

A water tank (open to the atmosphere) contains water to a depth of \(5 \mathrm{m} .\) A 25 -mm-diameter hole is punched in the bottom. Modeling the hole as square-edged, estimate the flow rate (L/s) exiting the tank. If you were to stick a short section of pipe into the hole, by how much would the flow rate change? If instead you were to machine the inside of the hole to give it a rounded edge \((r=5 \mathrm{mm})\), by how much would the flow rate change?

A fire nozzle is supplied through \(100 \mathrm{m}\) of \(3.5-\mathrm{cm}\) diameter, smooth, rubber-lined hose. Water from a hydrant is supplied to a booster pump on board the pumper truck at \(350 \mathrm{kPa}(\text { gage }) .\) At design conditions, the pressure at the nozzle inlet is 700 kPa (gage), and the pressure drop along the hose is 750 kPa per \(100 \mathrm{m}\) of length. Determine (a) the design flow rate, (b) the nozzle exit velocity, assuming no losses in the nozzle, and (c) the power required to drive the booster pump, if its efficiency is 70 percent.

Consider fully developed laminar flow between infinite parallel plates separated by gap width \(d=0.2\) in. The upper plate moves to the right with speed \(U_{2}=5 \mathrm{ft} / \mathrm{s}\); the lower plate moves to the left with speed \(U_{1}=2 \mathrm{ft}\) /s. The pressure gradient in the direction of flow is zero. Develop an expression for the velocity distribution in the gap. Find the volume flow rate per unit depth (gpm/ft) passing a given cross section.
See all solutions

Recommended explanations on Physics Textbooks

Electricity

Read Explanation

Waves Physics

Read Explanation

Measurements

Read Explanation

Scientific Method Physics

Read Explanation

Geometrical and Physical Optics

Read Explanation

Medical Physics

Read Explanation
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.