Answer:
The mass flow rate of the mixture in the manifold is 6.654 kg/min
Explanation;
In this question, we are asked to calculate mass flow rate of the mixture in the manifold
Please check attachment for complete solution and step by step explanation.
Answer:
R =
Explanation:
The mappings always involve a translation and a rotation of the matrix. Therefore, the rotation matrix will be given by:
Let and
be the the angles 60⁰ and 30⁰ respectively
that is = 60⁰ and
= 30⁰
The matrix is given by the following expression:
The angles can be evaluated and left in the surd form.
Answer:
The speed at point B is 5.33 m/s
The normal force at point B is 694 N
Explanation:
The length of the spring when the collar is in point A is equal to:
The length in point B is:
lB=0.2+0.2=0.4 m
The equation of conservation of energy is:
(eq. 1)
Where in point A: Tc = 1/2 mcVA^2, Ts=0, Vc=mcghA, Vs=1/2k(lA-lul)^2
in point B: Ts=0, Vc=0, Tc = 1/2 mcVB^2, Vs=1/2k(lB-lul)^2
Replacing in eq. 1:
Replacing values and clearing vB:
vB = 5.33 m/s
The balance forces acting in point B is:
Fc-NB-Fs=0
Replacing values and clearing NB:
NB = 694 N
Answer:
Part A
The mass plow rate, is approximately 97.0 lbm/s
Part B
The power used to overcome friction, is approximately 1.9 hp
Explanation:
The efficiency of the pump, η = 80%
The power input to the pump, P = 20 hp
The speed of the water through the pipe, v = 10 ft./s
The diameter of the pipe, d = 5.2 inches = 13/30 ft.
The free surface of the pool above the lake, h = 80 ft.
The density of the water, ρ = 62.4 lbm/ft.³
Part A
The mass plow rate, = Q × ρ
Where;
ρ = 62.4 lbm/ft³
Q = A × v
A = The cross-sectional area of the pipe
∴ Q = π·d²/4 × v = π × ((13/30 ft.)²)/4 × 10 ft.s ≈ 1.4748 ft.³/s
∴ The mass plow rate, ≈ 1.4748 ft.³/s × 62.4 lbm/ft.³ = 97.02752 lbm/s
The mass plow rate, ≈ 97.0 lbm/s
Part B
The power to pump the water at the given rate, =
·g·h
∴ = 97.02752 lbm/s × 32.1740 ft./s² × 80 ft. ≈ 14.1130725 Hp
≈ 14.1130725 Hp
The power output of the pump, = 0.8 × 20 hp = 16 hp
Therefore, the power used to overcome friction, =
-
∴ ≈ 16 hp - 14.1130725 Hp ≈ 1.8869275 hp
The power used to overcome friction, ≈ 1.9 hp