Ask Question, Ask an Expert

+1-415-315-9853

info@mywordsolution.com

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

Define the endurance limit of a bolt which is greater the

Define the endurance limit of a bolt ? Which is greater, the static yield strength or the endurance limit of the bolt? When will an increase in preload increase fatigue life? When will an increase in preload decrease fat ...

An athlete at high performance inhales of air at 10 atm and

An athlete at high performance inhales of air at 1.0 atm and 298 K at a respiration rate of 32 breaths per minute. If the exhaled and inhaled air contain 15.3 and 20.9% by volume of oxygen respectively, how many moles of ...

In problem compute the upward force on the device from

In Problem, compute the upward force on the device from water and air. Use the results of Problem as well as any other data given in that problem that you may need. Explain why you cannot profitably use Bernoulli's equat ...

While brewing beer a delinquent professor finds it

While brewing beer, a delinquent professor Finds it necessary to rapidly cool the "wort," a fermented malt mixture, from near the boiling point of water to room temperature. A 5.7 L sample of the wort at 363 K is combine ...

Water in an open cylindrical tank 15 ft in diameter

Water in an open cylindrical tank 15 ft in diameter discharges into the atmosphere through a nozzle 2 in. in diameter. Neglecting friction and the unsteadiness of the flow, find the time required for the water in the tan ...

1 using the expression for the gradient in polar

1. Using the expression for the gradient in polar coordinates (Appendix A), find the gradient of ψ(r,θ) when Where is the gradient maximum? The terms A and a are constant. 2. Given the following expression for the pressu ...

Earth is losing its supply of helium by escape from the

Earth is losing its supply of helium by escape from the atmosphere, because helium has a high median speed and (unlike hydrogen, which has even less mass) it does not chemically react to form heavier molecules as it difu ...

1 a slender vertical bar ab with pinned ends and length l

1. A slender vertical bar AB with pinned ends and length L is held between immovable supports. What increase ?T in the temperature of the bar will produce buckling? 2. A W2 × 87 structural steel column has a length of 12 ...

A 1 in times 10 in plank on a redwood deck has l 48 in

A 1 in × 10 in plank on a redwood deck has L = 48 in long and supported on three joists that rest on the ground and so do not bend. The joists act as pin/roller supports for the plank. If a 130 lb person stands on the pl ...

You are asked to design a cylindrical scuba tank with a

You are asked to design a cylindrical scuba tank with a radius R = 16 cm to a pressure of p = 12.0 MPa at a factor of safety of 2.0 with respect to the yield stress. The relevant tabulated yield values for the steel of w ...

  • 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

WalMart Identification of theory and critical discussion

Drawing on the prescribed text and/or relevant academic literature, produce a paper which discusses the nature of group

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