Other Math Answers

what are the conditions for flow to be irrotational.

The velocity components in a two dimensional flow are :
U = 8x^2 y - 8/3 y^3 And
V = -8xy^3 + 8/3 x^3.
Show that these velocity components represents a possible case of an irrotational flow.

Find the convective acceleration at the middle of a pipe which converges uniformly from 0.6 m diameter to 0.3 m diameter over 3 cm length. The rate of flow is 40 lit/s. If the rate of flow changes uniformly from 40 lit/s to 80 lit/s in 40 seconds, find the total acceleration at the middle of the pipe at 20th second.

A fluid flow is given by : V = x^2 yi - 2yz^2 j - ( zy^2 - 2z^3 /3 ) k. Prove that it is a case of possible steady incompressible fluid flow.

The velocity potential function φ, is given by φ = x2 - y^2 . Find the velocity components in x and y direction. Also show that φ represents a possible case of fluid flow.

The stream function for a two dimensional flow is given by ψ = 8xy, calculate the velocity at the point p(4, 5). Find the velocity potential function φ.

A 30 cm diameter pipe carries oil of sp. gr. 0.8 at a velocity of 2 m/s. At another section the diameter is 20 cm. Find the velocity at this section and also mass rate of flow of oil.

A 40 cm diameter pipe, conveying water, branches into two pipes of diameters 30 cm and 20 cm respectively. If the average velocity in the 40 cm diameter pipe is 3 m/s. Find the discharge in this pipe. Also determine the velocity in 20 cm pipe if the average velocity in 30 cm diameter pipe is 2 m/s.

The diameter of a pipe at the section 1 and 2 are 15 cm and 20 cm respectively. Find the discharge through the pipe if velocity of water at section 1 is 4 m/s. Determine also the velocity at section 2.

_____17. A rectangular solid whose dimensions are 4cm, 8cm, and 12cm is inscribed in a sphere. What is the diagonal of the rectangular solid?

a) 7.49 cm b) 8.94 cm c) 14.42 cm d) 14.97 cm

_____18. In question 17, what is the surface area of the sphere in 1?

a) 176.24 b) 251.09 c) 704.03 d) 1,405.25