HOMEWORK-3 (Due on 12/05/2016)
ET 354: Applied Fluid Mechanics
Fall 2016, Central Connecticut State University (Engineering)
Instructor: Dr. Brendan S. Mascarenhas
1. Equal points for each question. Maximum Points = 5.
Neglect air resistance and viscosity for the first 3 problems. Take acceleration due to gravity, g = 10m/s2 .
(a) A liquid of mass 5.0 kg is in a jar held at a height of 2.0 m above the
ground. Find the gravitational potential energy of the liquid in the jar.
(b) If the jar is slowly tilted so that the liquid is poured out of the jar, find
the velocity of the liquid when it reaches the ground.
(c) Find the time taken for the first particle of fluid to reach the ground from
the instant it leaves the lip of the jar.
(d) If the liquid in the jar is at room temperature, and right after pouring out
of the jar it collects in a shallow puddle on the ground would you expect
the temperature of the liquid in the puddle to be the same or different
from when it was in the jar? Briefly explain your answer.
(e) Would your answer to 1d above change if instead of being poured on the
ground the liquid was poured from the same height into another container
that rests on a vertical spring? Briefly explain your answer.
2. An airtight cylindrical tank has it’s axis vertical as shown in the figure1. The
tank has water filled in to to a height of 10.0 m. The gage pressure in the
tank above the water surface is 2 atmospheres. One end of a hose is connected
to a smooth circular opening at the bottom surface of the tank such that the
other end of the hose discharges water vertically upward into the atmosphere.
Neglecting mechanical energy losses, find the maximum height to which the
water jet could possibly rise. Take acceleration due to gravity = g = 10 m/s2 ,
density of water ρ = 103 kg/m3 , 1 atm = 105 N/m2 .
5 points
3. Consider the segment of circular cross-section pipe on non-uniform diameter as
shown in the figure 2. The centerline of the pipe is assumed to be horizontal.
Pgage = 2 atm
10 m
P = Patm
Water
Water jet
g = 10 m/s2
Figure 1:
Given that ρ is the density of air flowing (incompressible) through the pipe
and the pressures and cross-sectional areas at the entrance and the narrowest
section (throat) are P1 , A1 and P2 , A2 respectively
(a) show that the volumetric flow rate through the pipe can be expressed as
s
2 (P1 − P2 )
V̇ = A2
ρ (1 − A22 /A21 )
3 points
(b) Using the data provided in the figure and density of air, ρ = 1.2 kg/m3
determine the volume flow rate and the mass flow rate of air through the
pipe.
2 points
4. A cart of mass M has a curved deflector plate fixed to the back. The cart
is initially at rest on a smooth horizontal surface. A jet of water impinges
normally (perpendicular) on the deflector plate and is deflected at an angle of
θ to the back face of the cart as shown in figure 3. Note that after deflection,
the jet has a cross-section in the form of a doughnut as shown in the figure.
P 1 = 84.1kpa
P 2 = 81.3 6kpa
D1 = 0.066m D2 = 0.046m
Figure 2:
(a) Obtain an expression for the initial acceleration.
2.5 points
(b) Find the final velocity of the cart.
2.5 points
Total circumferential area o f jet leaving = A /2
Exit a ngle with b ack o f cart = 𝜃
Area o f jet incoming = A
𝜃
Mass = M kg
Mass flow rate = 𝑚̇
Density = ρ
𝜃
Smooth surface. No friction
Figure 3: