/*! 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 79 Consider the cylindrical weir of... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 79

Consider the cylindrical weir of diameter \(3 \mathrm{m}\) and length \(6 \mathrm{m} .\) If the fluid on the left has a specific gravity of \(1.6,\) and on the right has a specific gravity of \(0.8,\) find the magnitude and direction of the resultant force.

Short Answer

Expert verified
To solve this problem, we first calculate the pressures on both sides of the weir using the given specific gravity values and the formula for fluid pressure. Then, we calculate the forces due to these pressures and take the difference to find the resultant force. The direction of the resultant force is towards the side with the higher pressure. After calculating, we get the magnitude and direction of the resultant force.

Step by step solution

01

Calculate Pressures

First we need to calculate the pressures due to the fluids on the left and the right side of the weir. We know that the pressure due to a fluid column is given by \( P = \rho g h \), where \(\rho\) is the density, \(g\) is the gravity and \(h\) is the height. Using the specific gravity, we can find out the densities of the fluids. The density of a fluid is given by \( \text{Density} = \text{SG} \times \text{Density of water} \). The density of water is known to be \(1000 \, kg/m^{3}\).
02

Find Resultant

The resultant force will be the difference in the pressure forces on the left and right side. The Force due to pressure is given by \( F = P \times A \) where \(P\) is the pressure and \(A\) is the area. The area of the cylindrical weir is its length multiplied by its diameter.
03

Direction of the Resultant Force

The direction of the resultant force will be along the direction of the greater individual force.
04

Calculate Magnitude and Direction

Following the previous steps, calculate the magnitude and the direction of the resultant force.

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

A centrifugal micromanometer can be used to create small and accurate differential pressures in air for precise measurement work. The device consists of a pair of parallel disks that rotate to develop a radial pressure difference. There is no flow between the disks. Obtain an expression for pressure difference in terms of rotation speed, radius, and air density. Evaluate the speed of rotation required to develop a differential pressure of \(8 \mu \mathrm{m}\) of water using a device with a \(50 \mathrm{mm}\) radius.

A pail, \(400 \mathrm{mm}\) in diameter and \(400 \mathrm{mm}\) deep, weighs \(15 \mathrm{N}\) and contains \(200 \mathrm{mm}\) of water. The pail is swung in a vertical circle of \(1-\mathrm{m}\) radius at a speed of \(5 \mathrm{m} / \mathrm{s}\). Assume the water moves as a rigid body. At the instant when the pail is at the top of its trajectory, compute the tension in the string and the pressure on the bottom of the pail from the water.

Assuming the bulk modulus is constant for seawater, derive an expression for the density variation with depth, \(h\) below the surface. Show that the result may be written \\[ \rho \approx \rho_{0}+b h \\] where \(\rho_{0}\) is the density at the surface. Evaluate the constant \(b .\) Then, using the approximation, obtain an equation for the variation of pressure with depth below the surface. Determine the depth in feet at which the error in pressure predicted by the approximate solution is 0.01 percent.

A barometer accidentally contains 6.5 inches of water on top of the mercury column (so there is also water vapor instead of a vacuum at the top of the barometer). On a day when the temperature is \(70^{\circ} \mathrm{F}\), the mercury column height is 28.35 inches (corrected for thermal expansion). Determine the barometric pressure in psia. If the ambient temperature increased to \(85^{\circ} \mathrm{F}\) and the barometric pressure did not change, would the mercury column be longer, be shorter, or remain the same length? Justify your answer.

Gas bubbles are released from the regulator of a submerged scuba diver. What happens to the bubbles as they rise through the seawater? Explain.
See all solutions

Recommended explanations on Physics Textbooks

Electromagnetism

Read Explanation

Torque and Rotational Motion

Read Explanation

Translational Dynamics

Read Explanation

Astrophysics

Read Explanation

Modern Physics

Read Explanation

Electricity and Magnetism

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.