Manufacturing Processes

In summary: L1 be the length of the sprue. Let P2 be the pressure at the base of the sprue, V2 be the velocity at the base of the sprue, and L2 be the length of the sprue. The energy equation is then:P1 + ½*ρ*V1^2 + f*L1 = P2 + ½*ρ*V2^2 + f*L2where f is the friction factor. Assuming that the pressure at the top and base of the sprue are atmospheric, and the friction factor is 0.02 (typical for a smooth sand mold), the equation simplifies to:½*8000*V1^2 + 0
  • #1
Suitengu
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During pouring into a sand mold, the molten metal can be poured into the downsprue at a constant flow rate during the time it takes to fill the mold. At the end of pouring the sprue is filled and there is negligible metal in the pouring cup. The downsprue is 6 in. long. Its cross-sectional area at the top is 0.8 in^2 and the base is 0.6 in^2. The cross-sectional area leading from the sprue is also 0.6 in^2 and it is 8 in. long before leading into the mold cavity, whose volume is 65 in^3. The volume of the riser located along the runner near the mold cavity is 25 in^3. It takes a total of 3 sec to fill the entire mold. This is more than the theoretical time required, indicating a loss of velocity due to friction in the sprue and runner. Find

a)the theoretical velocity and flow rate at the base of the downsprue
b)the total volume of the mold
c)the actual velocity and flow rate at the base of the sprue and
d)the loss of head in the gating system due to friction

I guess my problem is i don't know how to calculate actual differently from theoretical as I only know one way to calculate which I am not even too sure of. Could someone give me a push to start off?
 
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  • #2
a) The theoretical velocity and flow rate at the base of the downsprue can be calculated using the Bernoulli equation. The Bernoulli equation states that the sum of the pressures, velocities, and potential (or gravitational) energies of a fluid must remain constant. Let P1 be the pressure at the top of the sprue, V1 be the velocity at the top of the sprue, and Z1 be the height of the top of the sprue above the base of the sprue. Let P2 be the pressure at the base of the sprue, V2 be the velocity at the base of the sprue, and Z2 be the height of the base of the sprue above the base of the sprue. The Bernoulli equation is then:P1 + ½*ρ*V1^2 + ρ*g*Z1 = P2 + ½*ρ*V2^2 + ρ*g*Z2where ρ is the density of the molten metal and g is the acceleration due to gravity. Assuming that the pressure at the top and base of the sprue are atmospheric, and the density of the molten metal is 8000 kg/m^3, the equation simplifies to:½*8000*V1^2 + 9.81*6 = ½*8000*V2^2 + 9.81*0Solving for V2 gives:V2 = 7.63 m/sThe flow rate at the base of the sprue can then be calculated by multiplying the velocity by the cross-sectional area of the sprue:Q = V2*A2 = 7.63*0.6 = 4.58 m^3/sb) The total volume of the mold is the volume of the cavity plus the volume of the riser. Vtotal = Vcavity + Vriser = 65 + 25 = 90 in^3c) The actual velocity and flow rate at the base of the sprue can be calculated using the energy equation. The energy equation states that the sum of the pressure, velocity, and friction losses in a pipe must remain constant. Let P1 be the pressure at the top of the sprue, V1 be the velocity at the top of
 
  • #3


a) The theoretical velocity can be calculated using the Bernoulli's equation, which states that the velocity of a fluid is inversely proportional to the cross-sectional area of the pipe it is flowing through. The equation is as follows:

v = (2gh)^1/2

Where, v is the velocity, g is the acceleration due to gravity (9.8 m/s^2), and h is the height difference between the top and base of the downsprue.

In this case, h = 6 in. = 0.1524 m

Therefore, the theoretical velocity at the base of the downsprue is:

v = (2*9.8*0.1524)^1/2 = 1.38 m/s

The flow rate can be calculated by multiplying the velocity with the cross-sectional area of the downsprue at the base, which is 0.6 in^2 = 0.00387 m^2.

Therefore, the theoretical flow rate is:

Q = v*A = 1.38*0.00387 = 0.00534 m^3/s

b) The total volume of the mold can be calculated by adding the volume of the mold cavity (65 in^3 = 1.065*10^-4 m^3) and the volume of the riser (25 in^3 = 4.10*10^-5 m^3).

Therefore, the total volume of the mold is 1.475*10^-4 m^3.

c) The actual velocity and flow rate at the base of the downsprue can be calculated by taking into account the loss of velocity due to friction in the sprue and runner. This can be done by using the Darcy-Weisbach equation, which relates the head loss due to friction with the flow rate, pipe length, and pipe diameter. The equation is as follows:

hL = f (L/D)*v^2/2g

Where, hL is the head loss, f is the Darcy-Weisbach friction factor, L is the length of the pipe, D is the diameter of the pipe, v is the velocity, and g is the acceleration due to gravity.

Assuming a friction factor of 0.02 (typical for sand casting), the head loss in the downsprue can be calculated as:

h
 

What is the purpose of manufacturing processes?

The purpose of manufacturing processes is to convert raw materials or components into finished products through a series of steps or operations. These processes can involve machining, casting, molding, forming, joining, and finishing.

What are the different types of manufacturing processes?

The main types of manufacturing processes include additive manufacturing, subtractive manufacturing, forming and shaping, joining, and surface treatment. Additive manufacturing involves building up layers of material to create a final product, while subtractive manufacturing involves removing material from a larger piece to achieve the desired shape. Forming and shaping processes involve altering the shape of a material through techniques such as casting, molding, and forging. Joining processes involve combining multiple components together, and surface treatment processes involve improving the appearance or properties of a material through techniques such as polishing, painting, or coating.

What factors influence the choice of a manufacturing process?

The choice of a manufacturing process is influenced by factors such as the type of material being used, the desired final product, the cost and efficiency of the process, and the expertise and resources available. Other factors may include the quantity of products needed, the complexity of the design, and any specific requirements or regulations for the product.

What are some common challenges in manufacturing processes?

Some common challenges in manufacturing processes include ensuring quality control, managing the cost and efficiency of the process, maintaining a safe working environment, and meeting production deadlines. Other challenges may include keeping up with technological advancements, addressing environmental concerns, and adapting to changes in consumer demands.

How do advances in technology impact manufacturing processes?

Advances in technology have greatly impacted manufacturing processes, making them more efficient, precise, and cost-effective. Automation, computer-aided design and manufacturing, and the use of advanced materials and techniques have all played a role in improving manufacturing processes. Additionally, technology has allowed for the development of new and innovative manufacturing methods, such as additive manufacturing, which have revolutionized the industry.

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