Answer: Question 1: Efficiency is 0.6944
Question 2: speed of similar pump is 2067rpm
Explanation:
Question 1:
Flow rate of pump 1 (Q1) = 300gpm
Flow rate of pump 2 (Q2) = 400gpm
Head of pump (H)= 55ft
Speed of pump1 (v1)= 1500rpm
Speed of pump2(v2) = ?
Diameter of impeller in pump 1= 15.5in = 0.3937m
Diameter of impeller in pump 2= 15in = 0.381
B.H.P= 6.0
Assuming cold water, S.G = 1.0
eff= (H x Q x S.G)/ 3960 x B.H.P
= (55x 300x 1)/3960x 6
= 0.6944
Question 2:
Q = A x V. (1)
A1 x v1 = A2 x V2. (2)
Since A1 = A2 = A ( since they are geometrically similar
A = Q1/V1 = Q2/V2. (3)
V1(m/s) = r x 2π x N(rpm)/60
= (0.3937x 2 x π x 1500)/2x 60
= 30.925m/s
Using equation (3)
V2 = (400 x 30.925)/300
= 41.2335m/s
To rpm:
N(rpm) = (60 x V(m/s))/2 x π x r
= (60 x 41.2335)/ 2× π × 0.1905
= 2067rpm.
First of all we need to convert everything into SI units.
Let's start with the initial angular speed,

. Keeping in mind that


we have

And we should also convert the angle covered by the centrifuge:

This is the angle covered by the centrifuge before it stops, so its final angular speed is

.
To solve the problem we can use the equivalent of

of an uniformly accelerated motion but for a rotational motion. It will be

And by substituting the numbers, we can find the value of

, the angular acceleration:
By Newton's second law,
<em>n</em> + (-<em>w</em>) = 0
<em>p</em> + (-<em>f</em> ) = (20 kg) (2 m/s²)
where <em>n</em> is the magnitude of the normal force, <em>w</em> is the weight of the box, <em>p</em> is the magnitude of the applied force (<em>p</em> for <u>p</u>ush or <u>p</u>ull), and <em>f</em> is the magnitude of the friction force.
Calculate the weight of the box:
<em>w</em> = (20 kg) (9.80 m/s²) = 196 N
Then
<em>n</em> = <em>w</em> = 196 N
and
<em>f</em> = <em>µ</em> <em>n</em> = 0.5 (196 N) = 98 N
Now solve for <em>p</em> :
<em>p</em> - 98 N = 40 N
<em>p</em> = 138 N
Answer:
1.00 m/s^2
Explanation:
The problem can be solved by using Newton's second law:

where
F is the net force acting on an object
m is the mass of the object
a is its acceleration
In this problem, F=35 N (the force applied by Amber) and

is the mass of the wagon + the brother, so the acceleration of the wagon and the brother is

Answer:
when the pencil is balanced on a point it is motionless due to net force only acting trough the center, but when we release the position we are changing the location of a pencil hence due to turning affect it will expericence torque and the angular acceleration produced.
for the complete answer the length and mass of pencil should be known i am giving the general expression for the calculation of angular acceleration
Explanation:
<h3>τ=Iα</h3><h3>τ= torque</h3><h3>I = inertia</h3><h3>α= angular acceleration</h3>
where
I= mL^2/3 (by geometry of pencil)
when the pencil is released it will experience force due to weight
F=mgsinθ
so τ=Fxd
τ=mgsin(10°)x(L/2)
then.
α=τ/I
α=mgsin(10°)xL/2÷(mL^2)/3