Ask Question, Ask an Expert


Ask Mechanical Engineering Expert

problem: Consider the triangular laminar D for given b and h shown below:

1617_triangular laminar.jpg

a) Find xL(s) and xR(s), the left and right ends of the elementary strip, of thickness ds, a distance s from the x-axis. Hence gives its width w(s) and the corresponding form for 1/2 [xR(s) + xL(s)].

b) Find, by direct integration, the area, A, of the lamina. Note we can regard the lamina as a rectangle from which two right-angled triangles are removed.

c) Find, by direct integration, the first moments of area, As|O, Ax|O, of the laminar. Hence find the position (xc; sc) of the centroid C relative to O.

d) Find, by direct integration, the second moments of area, Ass|O ; Axs|O of the laminar. Hence, using the parallel axis theorem, obtain Ass|C and Axs|C.

e) Suppose the triangular lamina is part of a vertical wall that separates fluid of density 1/2 from air at atmospheric pressure, p0. Also gravity, of acceleration g, acts in the downward vertical s-direction with the horizontal x-axis (s = 0) lying a depth s1 below the free surface. Find

i) The (resultant) hydrostatic force FN(s1) acting on the lamina.
ii) The total moments of hydrostatic force Ms and Mx about the x and s-axes.
iii) The position (¹x; ¹ s), of the centre of pressure CP relative to the origin O.
iv) Show that the centroid and centre of pressure lie on the same line.

problem: In the system shown below, the force exerted by the free jet issuing from the sharp-edged circular nozzle and impinging on the small circular plate is just sufficient to keep the (isosceles) triangular door closed against the water pressure. The depth of the water in the tank is kept fixed by using top-up water. The mass of the arm, the circular plate and door are negligible. The door and the plate are each rigidly fixed to the arm, through their centroids.

563_jet system.jpg

Neglect friction in both the water flow and the pivot, and take ρ = 1000 kg/m3 the density of water, and g = 9:81m/s2 the acceleration due to gravity. Give full details of your assumptions, symbolic working and numerical calculations.

(a) Neglecting fluid motion (you can use results from Qu. 1) find (i) the horizontal hydrostatic force FN acting on the door, and (ii) the line of action of the hydrostatic force.

(b) Using Bernoulli's equation find the jet speed VJ.

(c) Draw a control volume focused only on the circular plate, and analyzes the linear momentum equation to find the horizontal hydrodynamic force FR acting on the plate in terms of nozzle diameter d.

(d) Finally, use moments to find the value of the diameter d.

Mechanical Engineering, Engineering

  • Category:- Mechanical Engineering
  • Reference No.:- M9126

Have any Question? 

Related Questions in Mechanical Engineering

Assigned work clearly indicate all assumptions and

Assigned Work (Clearly indicate all assumptions and references) 1. A 500 m 2 light colored swimming pool is located at (a) normal suburban site, (b) well-sheltered site, where the measured wind speed at 10 m height is 3 ...

Fixed-price contracts where the contractor bids a fixed

Fixed-price contracts, where the contractor bids a fixed price to complete a system development, may be used to move project risk from client to contractor. If anything goes wrong, the contractor has to pay. Suggest how ...

Hot air rises but what happens to it as it rises through

Hot air rises, but what happens to it as it rises through our atmosphere? Given the number density function Eq. 14.33 and the temperature curve plotted in Fig. 14.3 to the surrounding atmosphere, calculate the Final temp ...

1 identify the terms that may arise from the ground

1. Identify the terms that may arise from the ground configurations of the atoms of elements of Period 2 and suggest the order of their energies. 2. Find the first-order corrections to the energies of the hydrogen atom t ...

List three ways to control preload directly what are the

List three ways to control preload directly ? What are the advantages of a bonded ultrasonic transducer? What is sometimes cited as a disadvantage? Can torque be used to tighten a 6 in. diameter bolt? If not, why not? Na ...

Define a shear joint define an axial shear joint define

Define a shear joint? Define an axial shear joint? Define faying surface? Define friction-type joint? Define bearing-type joint? Draw a graph illustrating the way a shear joint fails? Is bolt preload important in a shear ...

You have been introduced to a number of different tools

You have been introduced to a number of different tools that can be used to help IE's and MfgE's analyze and develop solutions to make processes more effective and efficient. Watch the video located at http://www.iienet2 ...

For the experimental pump data given belowqflow rate

For the experimental pump data given below: Q F low Rat e ( ???? /s) ???? Total Pressure (kPa) P IN Shaft power (kW) 0.0000 504.82 1.190 0.0004 481.50 1.318 0.0008 476.70 1.573 0.0012 471.50 1.828 0.0017 461.00 2.083 0.0 ...

For the bar in problem 1112 find the largest allowable

For the bar in Problem 11.12, find the largest allowable value of P if the allowable compressive stress is 250 MPa. Problem 11.12: A steel bar with the cross section shown and effective length L = 2.5 m is subjected to a ...

Complete the report with taking care the followingschapter

Complete the report with taking care the followings: Chapter 1 Air Pollution Historical Remarks What Is An Air Pollutant? Pollutant Emissions Primary Gaseous Pollutants Primary Particulate Matter Radioactive Pollutants S ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

Section onea in an atwood machine suppose two objects of

SECTION ONE (a) In an Atwood Machine, suppose two objects of unequal mass are hung vertically over a frictionless

Part 1you work in hr for a company that operates a factory

Part 1: You work in HR for a company that operates a factory manufacturing fiberglass. There are several hundred empl

Details on advanced accounting paperthis paper is intended

DETAILS ON ADVANCED ACCOUNTING PAPER This paper is intended for students to apply the theoretical knowledge around ac

Create a provider database and related reports and queries

Create a provider database and related reports and queries to capture contact information for potential PC component pro

Describe what you learned about the impact of economic

Describe what you learned about the impact of economic, social, and demographic trends affecting the US labor environmen